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Algebra

Quadratic Equations

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Quiz

Quadratic Equations Score: 0/10

1. Solve for x : 3x² + 18x - 81 = 0

1. Solve for x :

3x² + 18x - 81 = 0

A. x = 9 or x = - 9

B. x = 3 or x = - 9

C. x = 3 or x = - 27

D. None of the above

2. Solve for x : 12x² - 11x + 2 = 0

2. Solve for x :

12x² - 11x + 2 = 0

A. x = 4 or x =

\frac{3}{2}

B. x = 1 or x = 2

C. x =

\frac{1}{4}

or x =

\frac{2}{3}

D. None of the above

3. Solve for x : 2x ( 3x + 5 ) = 11

3. Solve for x :

2x ( 3x + 5 ) = 11

A. x =

\frac{- 5 + \sqrt[]{91}}{6}

or x =

\frac{- 5 - \sqrt[]{91}}{6}

B. x =

\frac{5 + \sqrt[]{91}}{6}

or x =

\frac{5 - \sqrt[]{91}}{6}

C. x = - 5 or x = 5

D. None of the above

4. Solve for x by completing the square: 2x² + x - 8 = 0

4. Solve for x by completing the square:

2x² + x - 8 = 0

A. x =

\frac{1 + \sqrt[]{65}}{4}

or x =

\frac{1 - \sqrt[]{65}}{4}

B. x =

\frac{- 1 + \sqrt[]{65}}{4}

or x =

\frac{- 1 - \sqrt[]{65}}{4}

C. x = - 1 or x = 1

D. None of the above

5. Solve for x by completing the square: - 2x² - 2x + $\frac{2}{3}$ = 0

5. Solve for x by completing the square:

- 2x² - 2x + $\frac{2}{3}$ = 0

A. x =

\frac{- 3 + \sqrt[]{21}}{6}

or x =

\frac{- 3 - \sqrt[]{21}}{6}

B. x = 3 or x = - 3

C. x =

\frac{3 + \sqrt[]{21}}{6}

or x =

\frac{3 - \sqrt[]{21}}{6}

D. None of the above

6. Solve for x by completing the square: x² - 6x - 39 = 0

6. Solve for x by completing the square:

x² - 6x - 39 = 0

A. x = - 3 + 4

\sqrt[]{3}

or x = - 3 - 4

\sqrt[]{3}

B. x = 3 + 4

\sqrt[]{3}

or x = 3 - 4

\sqrt[]{3}

C. x = 9 or x = - 9

D. None of the above

7. Solve the following inequality : 5 ( x² - 1 ) ≤ 2 ( 19x - 13 )

7. Solve the following inequality :

5 ( x² - 1 ) ≤ 2 ( 19x - 13 )

A. x ≤

\frac{3}{5}

or x ≥ 7

\frac{3}{5}

≤ x ≤ 7

C. x ≥

\frac{3}{5}

or x ≥ 7

D. None of the above

8. Solve the following inequality : - 15x² + x + 40 ≤ 0

8. Solve the following inequality :

- 15x² + x + 40 ≤ 0

A. -

\frac{5}{3}

≤ x ≤

\frac{8}{5}

B. -

\frac{8}{5}

≤ x ≤

\frac{5}{3}

C. x ≤ -

\frac{8}{5}

or x ≥

\frac{5}{3}

D. None of the above

9. Solve the following inequality : 8x ( x + 1 ) ≥ 4 ( 9 - x )

9. Solve the following inequality :

8x ( x + 1 ) ≥ 4 ( 9 - x )

A. - 3 ≤ x ≤

\frac{3}{2}

B. - 3 ≥ x ≥

\frac{3}{2}

C. x ≤ - 3 or x ≥

\frac{3}{2}

D. None of the above

10. Solve the following inequality : 5x ( 4x + 5 ) < 4 ( x - 1 )

10. Solve the following inequality :

5x ( 4x + 5 ) < 4 ( x - 1 )

A. -

\frac{4}{5}

< x < -

\frac{1}{4}

\frac{1}{4}

< x <

\frac{4}{5}

C. x < -

\frac{4}{5}

or x > -

\frac{1}{4}

D. None of the above

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Quiz Results

Your score is 0 out of 10

Solutions

Quadratic Equations Question 1 of 10

1. Solve for x : 3x² + 18x - 81 = 0

1. Solve for x :

3x² + 18x - 81 = 0

A. x = 9 or x = - 9

B. x = 3 or x = - 9

C. x = 3 or x = - 27

D. None of the above

Correct Answer
Option B

Detailed Solution

Solution Details

Given 3x² + 18x - 81 = 0

• 3x² + 18x - 81 = x² + 6x - 27 = 0

• ( x - 3 ) ( x + 9 ) = 0

• ( x - 3 ) = 0 or ( x + 9 ) = 0

∴ x = 3 or x = - 9

For more info please see

Quadratic Equations

Quadratic Equations Question 2 of 10

2. Solve for x : 12x² - 11x + 2 = 0

2. Solve for x :

12x² - 11x + 2 = 0

A. x = 4 or x =

\frac{3}{2}

B. x = 1 or x = 2

C. x =

\frac{1}{4}

or x =

\frac{2}{3}

D. None of the above

Correct Answer
Option C

Detailed Solution

Solution Details

Given 12x² - 11x + 2 = 0

• 12x² - 11x + 2 = 0

• ( 4x - 1 ) ( 3x - 2 ) = 0

• ( 4x - 1 ) = 0 or ( 3x - 2 ) = 0

∴ x = $\frac{1}{4}$ or x = $\frac{2}{3}$

For more info please see

Quadratic Equations

Quadratic Equations Question 3 of 10

3. Solve for x : 2x ( 3x + 5 ) = 11

3. Solve for x :

2x ( 3x + 5 ) = 11

A. x =

\frac{- 5 + \sqrt[]{91}}{6}

or x =

\frac{- 5 - \sqrt[]{91}}{6}

B. x =

\frac{5 + \sqrt[]{91}}{6}

or x =

\frac{5 - \sqrt[]{91}}{6}

C. x = - 5 or x = 5

D. None of the above

Correct Answer
Option A

Detailed Solution

Solution Details

Given 2x ( 3x + 5 ) = 11

• 2x ( 3x + 5 ) = 11

• 6x² + 10x - 11 = 0

• x = $\frac{– b ± \sqrt[]{b 2 – 4ac}}{2a}$ The equation cannot be factorised so we use the quadratic formula

• x = $\frac{– 10 ± \sqrt[]{( 10 ) 2 – 4 ( 6 ) ( - 11 )}}{2 ( 6 )}$ = $\frac{– 10 ± \sqrt[]{364}}{12}$ = $\frac{– 10 ± 2 \sqrt[]{91}}{12}$ = $\frac{– 5 ± \sqrt[]{91}}{6}$

∴ x = $\frac{– 5 + \sqrt[]{91}}{6}$ or x = $\frac{– 5 – \sqrt[]{91}}{6}$

For more info please see

Quadratic Equations

Given 2x ( 3x + 5 ) = 11

• 2x ( 3x + 5 ) = 11

• 6x² + 10x - 11 = 0

• x = $\frac{– b ± \sqrt[]{b 2 – 4ac}}{2a}$

The equation cannot be factorised so we use the quadratic formula

• x = $\frac{– 10 ± \sqrt[]{( 10 ) 2 – 4 ( 6 ) ( - 11 )}}{2 ( 6 )}$

= $\frac{– 10 ± \sqrt[]{364}}{12}$

= $\frac{– 10 ± 2 \sqrt[]{91}}{12}$

= $\frac{– 5 ± \sqrt[]{91}}{6}$

∴ x = $\frac{– 5 + \sqrt[]{91}}{6}$ or x = $\frac{– 5 – \sqrt[]{91}}{6}$

For more info please see

Quadratic Equations

Quadratic Equations Question 4 of 10

4. Solve for x by completing the square: 2x² + x - 8 = 0

4. Solve for x by completing the square:

2x² + x - 8 = 0

A. x =

\frac{1 + \sqrt[]{65}}{4}

or x =

\frac{1 - \sqrt[]{65}}{4}

B. x =

\frac{- 1 + \sqrt[]{65}}{4}

or x =

\frac{- 1 - \sqrt[]{65}}{4}

C. x = - 1 or x = 1

D. None of the above

Correct Answer
Option B

Detailed Solution

Solution Details

Given 2x² + x - 8 = 0

• 2x² + x - 8 = 0

• x² + $\frac{1}{2}$ x - 4 = 0

• x² + $\frac{1}{2}$ x + $\frac{1}{16}$ = 4 + $\frac{1}{16}$

• ( x + $\frac{1}{4}$ ) ² = $\frac{65}{16}$

• x + $\frac{1}{4}$ = ± $\frac{\sqrt[]{65}}{4}$

• x = $\frac{- 1 ± \sqrt[]{65}}{4}$

∴ x = $\frac{- 1 + \sqrt[]{65}}{4}$ or x = $\frac{- 1 - \sqrt[]{65}}{4}$

For more info please see

Quadratic Equations

Quadratic Equations Question 5 of 10

5. Solve for x by completing the square: - 2x² - 2x + $\frac{2}{3}$ = 0

5. Solve for x by completing the square:

- 2x² - 2x + $\frac{2}{3}$ = 0

A. x =

\frac{- 3 + \sqrt[]{21}}{6}

or x =

\frac{- 3 - \sqrt[]{21}}{6}

B. x = 3 or x = - 3

C. x =

\frac{3 + \sqrt[]{21}}{6}

or x =

\frac{3 - \sqrt[]{21}}{6}

D. None of the above

Correct Answer
Option A

Detailed Solution

Solution Details

Given - 2x² - 2x + $\frac{2}{3}$ = 0

• - 2x² - 2x + $\frac{2}{3}$ = 0

• x² + x - $\frac{1}{3}$ = 0

• x² + x + $\frac{1}{4}$ = $\frac{1}{3}$ + $\frac{1}{4}$

• ( x + $\frac{1}{2}$ ) ² = $\frac{7}{12}$

• x + $\frac{1}{2}$ = ± $\frac{\sqrt[]{7}}{\sqrt[]{12}}$

• x + $\frac{1}{2}$ = ± $\frac{\sqrt[]{7} \sqrt[]{12}}{\sqrt[]{12} \sqrt[]{12}}$

• x + $\frac{1}{2}$ = ± $\frac{\sqrt[]{84}}{12}$

• x = $\frac{- 6 ± \sqrt[]{4 × 21}}{12}$

∴ x = $\frac{- 3 + \sqrt[]{21}}{6}$ or x = $\frac{- 3 - \sqrt[]{21}}{6}$

For more info please see

Quadratic Equations

Quadratic Equations Question 6 of 10

6. Solve for x by completing the square: x² - 6x - 39 = 0

6. Solve for x by completing the square:

x² - 6x - 39 = 0

A. x = - 3 + 4

\sqrt[]{3}

or x = - 3 - 4

\sqrt[]{3}

B. x = 3 + 4

\sqrt[]{3}

or x = 3 - 4

\sqrt[]{3}

C. x = 9 or x = - 9

D. None of the above

Correct Answer
Option B

Detailed Solution

Solution Details

Given x² - 6x - 39 = 0

• x² - 6x - 39 = 0

• x² - 6x + 9 = 39 + 9

• ( x - 3 )² = 48

• x - 3 = ± $\sqrt[]{48}$

• x = 3 ± 4 $\sqrt[]{3}$

∴ x = 3 + 4 $\sqrt[]{3}$ or x = 3 - 4 $\sqrt[]{3}$

For more info please see

Quadratic Equations

Quadratic Equations Question 7 of 10

7. Solve the following inequality : 5 ( x² - 1 ) ≤ 2 ( 19x - 13 )

7. Solve the following inequality :

5 ( x² - 1 ) ≤ 2 ( 19x - 13 )

A. x ≤

\frac{3}{5}

or x ≥ 7

\frac{3}{5}

≤ x ≤ 7

C. x ≥

\frac{3}{5}

or x ≥ 7

D. None of the above

Correct Answer
Option B

Detailed Solution

Solution Details

Given 5 ( x² - 1 ) ≤ 2 ( 19x - 13 )

• 5 ( x² - 1 ) ≤ 2 ( 19x - 13 )

• 5x² - 5 ≤ 38x - 26

• 5x² - 38x + 21 ≤ 0

• ( 5x - 3 ) ( x - 7 ) ≤ 0

• 5x² - 38x + 21 = 0 at x = $\frac{3}{5}$ and x = 7

+0-0+

||||

| $\frac{3}{5}$ 7|

We have to find values of x where 5x² - 38x + 21 ≤ 0.

∴ $\frac{3}{5}$ ≤ x ≤ 7

For more info please see

Quadratic Equations

Quadratic Equations Question 8 of 10

8. Solve the following inequality : - 15x² + x + 40 ≤ 0

8. Solve the following inequality :

- 15x² + x + 40 ≤ 0

A. -

\frac{5}{3}

≤ x ≤

\frac{8}{5}

B. -

\frac{8}{5}

≤ x ≤

\frac{5}{3}

C. x ≤ -

\frac{8}{5}

or x ≥

\frac{5}{3}

D. None of the above

Correct Answer
Option C

Detailed Solution

Solution Details

Given - 15x² + x + 40 ≤ 0

• - 15x² + x + 40 ≤ 0

• 15x² - x - 40 ≥ 0

• ( 3x - 5 ) ( 5x + 8 ) ≥ 0

• 15x² - x - 40 ≥ 0 at x = $\frac{5}{3}$ and x = - $\frac{8}{5}$

+0-0+

||||

|- $\frac{8}{5}$ $\frac{5}{3}$ |

We have to find values of x where 15x² - x - 40 ≥ 0.

∴ x ≤ - $\frac{8}{5}$ or x ≥ $\frac{5}{3}$

For more info please see

Quadratic Equations

Quadratic Equations Question 9 of 10

9. Solve the following inequality : 8x ( x + 1 ) ≥ 4 ( 9 - x )

9. Solve the following inequality :

8x ( x + 1 ) ≥ 4 ( 9 - x )

A. - 3 ≤ x ≤

\frac{3}{2}

B. - 3 ≥ x ≥

\frac{3}{2}

C. x ≤ - 3 or x ≥

\frac{3}{2}

D. None of the above

Correct Answer
Option C

Detailed Solution

Solution Details

Given 8x ( x + 1 ) ≥ 4 ( 9 - x )

• 8x ( x + 1 ) ≥ 4 ( 9 - x )

• 8x² + 8x ≥ 36 - 4x

• 8x² + 12x - 36 ≥ 0

• 2x² + 3x - 9 ≥ 0

• ( 2x - 3 ) ( x + 3 ) ≥ 0

• 2x² + 3x - 9 ≥ 0 at x = $\frac{3}{2}$ and x = - 3

+0-0+

||||

|- 3 $\frac{3}{2}$ |

We have to find values of x where 2x² + 3x - 9 ≥ 0.

∴ x ≤ - 3 or x ≥ $\frac{3}{2}$

For more info please see

Quadratic Equations

Quadratic Equations Question 10 of 10

10. Solve the following inequality : 5x ( 4x + 5 ) < 4 ( x - 1 )

10. Solve the following inequality :

5x ( 4x + 5 ) < 4 ( x - 1 )

A. -

\frac{4}{5}

< x < -

\frac{1}{4}

\frac{1}{4}

< x <

\frac{4}{5}

C. x < -

\frac{4}{5}

or x > -

\frac{1}{4}

D. None of the above

Correct Answer
Option A

Detailed Solution

Solution Details

Given 5x ( 4x + 5 ) < 4 ( x - 1 )

• 5x ( 4x + 5 ) < 4 ( x - 1 )

• 20x² + 25x < 4x - 4

• 20x² + 21x + 4 < 0

• ( 5x + 4 ) ( 4x + 1 ) < 0

• 20x² + 21x + 4 = 0 at x = - $\frac{4}{5}$ and x = - $\frac{1}{4}$

+0-0+

||||

|- $\frac{4}{5}$ - $\frac{1}{4}$ |

We have to find values of x where 20x² + 21x + 4 < 0.

∴ - $\frac{4}{5}$ < x < - $\frac{1}{4}$

For more info please see

Quadratic Equations

Quiz

Algebra

Quadratic Equations

Quiz Quidelines

Quiz

1. Solve for x : 3x 2 + 18x - 81 = 0

1. Solve for x : 3x 2 + 18x - 81 = 0

1. Solve for x : 3x 2 + 18x - 81 = 0

2. Solve for x : 12x 2 - 11x + 2 = 0

2. Solve for x : 12x 2 - 11x + 2 = 0

2. Solve for x : 12x 2 - 11x + 2 = 0

3. Solve for x : 2x ( 3x + 5 ) = 11

3. Solve for x : 2x ( 3x + 5 ) = 11

3. Solve for x : 2x ( 3x + 5 ) = 11

4. Solve for x by completing the square: 2x 2 + x - 8 = 0

4. Solve for x by completing the square: 2x 2 + x - 8 = 0

4. Solve for x by completing the square: 2x 2 + x - 8 = 0

5. Solve for x by completing the square: - 2x 2 - 2x + 2 3 = 0

5. Solve for x by completing the square: - 2x 2 - 2x + 2 3 = 0

5. Solve for x by completing the square: - 2x 2 - 2x + 2 3 = 0

6. Solve for x by completing the square: x 2 - 6x - 39 = 0

6. Solve for x by completing the square: x 2 - 6x - 39 = 0

6. Solve for x by completing the square: x 2 - 6x - 39 = 0

7. Solve the following inequality : 5 ( x 2 - 1 ) ≤ 2 ( 19x - 13 )

7. Solve the following inequality : 5 ( x 2 - 1 ) ≤ 2 ( 19x - 13 )

7. Solve the following inequality : 5 ( x 2 - 1 ) ≤ 2 ( 19x - 13 )

8. Solve the following inequality : - 15x 2 + x + 40 ≤ 0

8. Solve the following inequality : - 15x 2 + x + 40 ≤ 0

8. Solve the following inequality : - 15x 2 + x + 40 ≤ 0

9. Solve the following inequality : 8x ( x + 1 ) ≥ 4 ( 9 - x )

9. Solve the following inequality : 8x ( x + 1 ) ≥ 4 ( 9 - x )

9. Solve the following inequality : 8x ( x + 1 ) ≥ 4 ( 9 - x )

10. Solve the following inequality : 5x ( 4x + 5 ) < 4 ( x - 1 )

10. Solve the following inequality : 5x ( 4x + 5 ) < 4 ( x - 1 )

10. Solve the following inequality : 5x ( 4x + 5 ) < 4 ( x - 1 )

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Quiz Results

Solutions

1. Solve for x : 3x 2 + 18x - 81 = 0

1. Solve for x : 3x 2 + 18x - 81 = 0

1. Solve for x : 3x 2 + 18x - 81 = 0

Correct Answer Option B

Detailed Solution

Solution Details

Given 3x 2 + 18x - 81 = 0

• 3x 2 + 18x - 81 = x 2 + 6x - 27 = 0 • ( x - 3 ) ( x + 9 ) = 0 • ( x - 3 ) = 0 or ( x + 9 ) = 0 ∴ x = 3 or x = - 9

2. Solve for x : 12x 2 - 11x + 2 = 0

2. Solve for x : 12x 2 - 11x + 2 = 0

2. Solve for x : 12x 2 - 11x + 2 = 0

Correct Answer Option C

Detailed Solution

Solution Details

Given 12x 2 - 11x + 2 = 0

• 12x 2 - 11x + 2 = 0 • ( 4x - 1 ) ( 3x - 2 ) = 0 • ( 4x - 1 ) = 0 or ( 3x - 2 ) = 0 ∴ x = 1 4 or x = 2 3

3. Solve for x : 2x ( 3x + 5 ) = 11

3. Solve for x : 2x ( 3x + 5 ) = 11

3. Solve for x : 2x ( 3x + 5 ) = 11

Correct Answer Option A

Detailed Solution

Solution Details

Given 2x ( 3x + 5 ) = 11

• 2x ( 3x + 5 ) = 11 • 6x 2 + 10x - 11 = 0 • x = – b ± b 2 – 4ac 2a The equation cannot be factorised so we use the quadratic formula • x = – 10 ± ( 10 ) 2 – 4 ( 6 ) ( - 11 ) 2 ( 6 ) = – 10 ± 364 12 = – 10 ± 2 91 12 = – 5 ± 91 6 ∴ x = – 5 + 91 6 or x = – 5 – 91 6

Given 2x ( 3x + 5 ) = 11

• 2x ( 3x + 5 ) = 11 • 6x 2 + 10x - 11 = 0 • x = – b ± b 2 – 4ac 2a The equation cannot be factorised so we use the quadratic formula • x = – 10 ± ( 10 ) 2 – 4 ( 6 ) ( - 11 ) 2 ( 6 ) = – 10 ± 364 12 = – 10 ± 2 91 12 = – 5 ± 91 6 ∴ x = – 5 + 91 6 or x = – 5 – 91 6

4. Solve for x by completing the square: 2x 2 + x - 8 = 0

4. Solve for x by completing the square: 2x 2 + x - 8 = 0

4. Solve for x by completing the square: 2x 2 + x - 8 = 0

Correct Answer Option B

Detailed Solution

Solution Details

Given 2x 2 + x - 8 = 0

• 2x 2 + x - 8 = 0 • x 2 + 1 2 x - 4 = 0 • x 2 + 1 2 x + 1 16 = 4 + 1 16 • ( x + 1 4 ) 2 = 65 16 • x + 1 4 = ± 65 4 • x = - 1 ± 65 4 ∴ x = - 1 + 65 4 or x = - 1 - 65 4

5. Solve for x by completing the square: - 2x 2 - 2x + 2 3 = 0

5. Solve for x by completing the square: - 2x 2 - 2x + 2 3 = 0

5. Solve for x by completing the square: - 2x 2 - 2x + 2 3 = 0

Correct Answer Option A

Detailed Solution

Solution Details

Given - 2x 2 - 2x + 2 3 = 0

• - 2x 2 - 2x + 2 3 = 0 • x 2 + x - 1 3 = 0 • x 2 + x + 1 4 = 1 3 + 1 4 • ( x + 1 2 ) 2 = 7 12 • x + 1 2 = ± 7 12 • x + 1 2 = ± 7 12 12 12 • x + 1 2 = ± 84 12 • x = - 6 ± 4 × 21 12 ∴ x = - 3 + 21 6 or x = - 3 - 21 6

1. Solve for x : 3x² + 18x - 81 = 0

1. Solve for x : 3x² + 18x - 81 = 0

1. Solve for x :

3x² + 18x - 81 = 0

2. Solve for x : 12x² - 11x + 2 = 0

2. Solve for x : 12x² - 11x + 2 = 0

2. Solve for x :

12x² - 11x + 2 = 0

3. Solve for x :

2x ( 3x + 5 ) = 11

4. Solve for x by completing the square: 2x² + x - 8 = 0

4. Solve for x by completing the square: 2x² + x - 8 = 0

4. Solve for x by completing the square:

2x² + x - 8 = 0

5. Solve for x by completing the square: - 2x² - 2x + $\frac{2}{3}$ = 0

5. Solve for x by completing the square: - 2x² - 2x + $\frac{2}{3}$ = 0

5. Solve for x by completing the square:

- 2x² - 2x + $\frac{2}{3}$ = 0

6. Solve for x by completing the square: x² - 6x - 39 = 0

6. Solve for x by completing the square: x² - 6x - 39 = 0

6. Solve for x by completing the square:

x² - 6x - 39 = 0

7. Solve the following inequality : 5 ( x² - 1 ) ≤ 2 ( 19x - 13 )

7. Solve the following inequality : 5 ( x² - 1 ) ≤ 2 ( 19x - 13 )

7. Solve the following inequality :

5 ( x² - 1 ) ≤ 2 ( 19x - 13 )

8. Solve the following inequality : - 15x² + x + 40 ≤ 0

8. Solve the following inequality : - 15x² + x + 40 ≤ 0

8. Solve the following inequality :

- 15x² + x + 40 ≤ 0

9. Solve the following inequality :

8x ( x + 1 ) ≥ 4 ( 9 - x )

10. Solve the following inequality :

5x ( 4x + 5 ) < 4 ( x - 1 )

1. Solve for x : 3x² + 18x - 81 = 0

1. Solve for x : 3x² + 18x - 81 = 0

1. Solve for x :

3x² + 18x - 81 = 0

Correct Answer
Option B

Given 3x² + 18x - 81 = 0

• 3x² + 18x - 81 = x² + 6x - 27 = 0

• ( x - 3 ) ( x + 9 ) = 0

• ( x - 3 ) = 0 or ( x + 9 ) = 0

∴ x = 3 or x = - 9

2. Solve for x : 12x² - 11x + 2 = 0

2. Solve for x : 12x² - 11x + 2 = 0

2. Solve for x :

12x² - 11x + 2 = 0

Correct Answer
Option C

Given 12x² - 11x + 2 = 0

• 12x² - 11x + 2 = 0

• ( 4x - 1 ) ( 3x - 2 ) = 0

• ( 4x - 1 ) = 0 or ( 3x - 2 ) = 0

∴ x = $\frac{1}{4}$ or x = $\frac{2}{3}$

3. Solve for x :

2x ( 3x + 5 ) = 11

Correct Answer
Option A

4. Solve for x by completing the square: 2x² + x - 8 = 0

4. Solve for x by completing the square: 2x² + x - 8 = 0

4. Solve for x by completing the square:

2x² + x - 8 = 0

Correct Answer
Option B

Given 2x² + x - 8 = 0

5. Solve for x by completing the square: - 2x² - 2x + $\frac{2}{3}$ = 0

5. Solve for x by completing the square: - 2x² - 2x + $\frac{2}{3}$ = 0

5. Solve for x by completing the square:

- 2x² - 2x + $\frac{2}{3}$ = 0

Correct Answer
Option A

Given - 2x² - 2x + $\frac{2}{3}$ = 0

6. Solve for x by completing the square: x² - 6x - 39 = 0

6. Solve for x by completing the square: x² - 6x - 39 = 0

6. Solve for x by completing the square:

x² - 6x - 39 = 0

Correct Answer
Option B

Given x² - 6x - 39 = 0

• x² - 6x - 39 = 0

• x² - 6x + 9 = 39 + 9

• ( x - 3 )² = 48

• x - 3 = ± $\sqrt[]{48}$

• x = 3 ± 4 $\sqrt[]{3}$

∴ x = 3 + 4 $\sqrt[]{3}$ or x = 3 - 4 $\sqrt[]{3}$

7. Solve the following inequality : 5 ( x² - 1 ) ≤ 2 ( 19x - 13 )

7. Solve the following inequality : 5 ( x² - 1 ) ≤ 2 ( 19x - 13 )

7. Solve the following inequality :

5 ( x² - 1 ) ≤ 2 ( 19x - 13 )

Correct Answer
Option B

Given 5 ( x² - 1 ) ≤ 2 ( 19x - 13 )

8. Solve the following inequality : - 15x² + x + 40 ≤ 0

8. Solve the following inequality : - 15x² + x + 40 ≤ 0

8. Solve the following inequality :

- 15x² + x + 40 ≤ 0

Correct Answer
Option C

Given - 15x² + x + 40 ≤ 0

9. Solve the following inequality :

8x ( x + 1 ) ≥ 4 ( 9 - x )

Correct Answer
Option C

10. Solve the following inequality :

5x ( 4x + 5 ) < 4 ( x - 1 )

Correct Answer
Option A