Quiz

Algebra

Nature of Roots

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Nature of Roots Score: 0/10

1. What is the nature of roots of the equation : x² + 8x + 16 = 0

1. What is the nature of roots of the equation :

x² + 8x + 16 = 0

A.Non-Real

B.Rational

C.Irrational

D.None of the above

2. What is the nature of roots of the equation : x² - 5x + 3 = 0

2. What is the nature of roots of the equation :

x² - 5x + 3 = 0

A.Non-Real

B.Rational

C.Irrational

D.None of the above

3. What is the nature of roots of the equation : 2x² - 2x + 1 = 0

3. What is the nature of roots of the equation :

2x² - 2x + 1 = 0

A.Non-Real

B.Rational

C.Irrational

D.None of the above

4. For which values of k will the equation x² + x = k have no real roots ?

4. For which values of k will the equation

x² + x = k

have no real roots ?

A.k < -

\frac{1}{4}

B.k ≤ -

\frac{1}{4}

C.k > -

\frac{1}{4}

D.None of the above

5. The roots of a quadratic equation are : x = $\frac{3 ± \sqrt[]{– k – 4}}{2}$

For which values of k are the roots real

5. The roots of a quadratic equation are :

x = $\frac{3 ± \sqrt[]{– k – 4}}{2}$

For which values of k are the roots real

A.k = - 4

B.k ≥ - 4

C.k ≤ - 4

D.None of the above

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Quiz Results

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Solutions

Nature of Roots Question 1 of 5

1. What is the nature of roots of the equation : x² + 8x + 16 = 0

1. What is the nature of roots of the equation :

x² + 8x + 16 = 0

A.Non-Real

B.Rational

C.Irrational

D.None of the above

Correct Answer
Option B

Detailed Solution

Solution Details

Given x² + 8x + 16 = 0

• x² + 8x + 16 = 0

a = 1, b = 8, c = 16

• Δ = b² - 4ac

= 8² - 4 ( 1 ) ( 16 ) = 0

• Δ = 0

∴ The roots are Rational

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Nature of Roots

Nature of Roots Question 2 of 5

2. What is the nature of roots of the equation : x² - 5x + 3 = 0

2. What is the nature of roots of the equation :

x² - 5x + 3 = 0

A.Non-Real

B.Rational

C.Irrational

D.None of the above

Correct Answer
Option C

Detailed Solution

Solution Details

Given x² - 5x + 3 = 0

• x² - 5x + 3 = 0

a = 1, b = - 5, c = 3

• Δ = b² - 4ac

= ( - 5 )² - 4 ( 1 ) ( 3 ) = 13

• Δ > 0

∴ The roots are Irrational

For more info please see

Nature of Roots

Nature of Roots Question 3 of 5

3. What is the nature of roots of the equation : 2x² - 2x + 1 = 0

3. What is the nature of roots of the equation :

2x² - 2x + 1 = 0

A.Non-Real

B.Rational

C.Irrational

D.None of the above

Correct Answer
Option A

Detailed Solution

Solution Details

Given 2x² - 2x + 1 = 0

• 2x² - 2x + 1 = 0

a = 2, b = - 2, c = 1

• Δ = b² - 4ac

= ( - 2 )² - 4 ( 2 ) ( 1 ) = - 4

• Δ < 0

∴ The roots are Non-Real

For more info please see

Nature of Roots

Nature of Roots Question 4 of 5

4. For which values of k will the equation x² + x = k have no real roots ?

4. For which values of k will the equation

x² + x = k

have no real roots ?

A.k < -

\frac{1}{4}

B.k ≤ -

\frac{1}{4}

C.k > -

\frac{1}{4}

D.None of the above

Correct Answer
Option A

Detailed Solution

Solution Details

Given x² + x = k

• x² + x - k = 0

a = 1, b = 1, c = - k

• Δ < 0

b² - 4ac < 0

( 1 )² - 4 ( 1 ) ( - k ) < 0

1 + 4k < 0

4k < - 1

∴ k < - $\frac{1}{4}$

For more info please see

Nature of Roots

Nature of Roots Question 5 of 5

5. The roots of a quadratic equation are : x = $\frac{3 ± \sqrt[]{– k – 4}}{2}$

For which values of k are the roots real

5. The roots of a quadratic equation are :

x = $\frac{3 ± \sqrt[]{– k – 4}}{2}$

For which values of k are the roots real

A.k = - 4

B.k ≥ - 4

C.k ≤ - 4

D.None of the above

Correct Answer
Option C

Detailed Solution

Solution Details

Given x = $\frac{3 ± \sqrt[]{– k – 4}}{2}$

• x = $\frac{3 ± \sqrt[]{– k – 4}}{2}$

• - k - 4 ≥ 0

• - k ≥ 4

∴ k ≤ - 4

For more info please see

Nature of Roots

Quiz

Algebra

Nature of Roots

Quiz Quidelines

Quiz

1. What is the nature of roots of the equation : x2 + 8x + 16 = 0

1. What is the nature of roots of the equation : x2 + 8x + 16 = 0

1. What is the nature of roots of the equation : x2 + 8x + 16 = 0

2. What is the nature of roots of the equation : x2 - 5x + 3 = 0

2. What is the nature of roots of the equation : x2 - 5x + 3 = 0

2. What is the nature of roots of the equation : x2 - 5x + 3 = 0

3. What is the nature of roots of the equation : 2x2 - 2x + 1 = 0

3. What is the nature of roots of the equation : 2x2 - 2x + 1 = 0

3. What is the nature of roots of the equation : 2x2 - 2x + 1 = 0

4. For which values of k will the equation x2 + x = k have no real roots ?

4. For which values of k will the equation x2 + x = k have no real roots ?

4. For which values of k will the equation x2 + x = k have no real roots ?

5. The roots of a quadratic equation are : x = 3 ± – k – 4 2 For which values of k are the roots real

5. The roots of a quadratic equation are : x = 3 ± – k – 4 2 For which values of k are the roots real

5. The roots of a quadratic equation are : x = 3 ± – k – 4 2 For which values of k are the roots real

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Quiz Results

Solutions

1. What is the nature of roots of the equation : x2 + 8x + 16 = 0

1. What is the nature of roots of the equation : x2 + 8x + 16 = 0

1. What is the nature of roots of the equation : x2 + 8x + 16 = 0

Correct Answer Option B

Detailed Solution

Solution Details

Given x2 + 8x + 16 = 0

• x2 + 8x + 16 = 0 a = 1, b = 8, c = 16

• Δ = b2 - 4ac = 82 - 4 ( 1 ) ( 16 ) = 0

• Δ = 0

∴ The roots are Rational

2. What is the nature of roots of the equation : x2 - 5x + 3 = 0

2. What is the nature of roots of the equation : x2 - 5x + 3 = 0

2. What is the nature of roots of the equation : x2 - 5x + 3 = 0

Correct Answer Option C

Detailed Solution

Solution Details

Given x2 - 5x + 3 = 0

• x2 - 5x + 3 = 0 a = 1, b = - 5, c = 3

• Δ = b2 - 4ac = ( - 5 )2 - 4 ( 1 ) ( 3 ) = 13

• Δ > 0

∴ The roots are Irrational

3. What is the nature of roots of the equation : 2x2 - 2x + 1 = 0

3. What is the nature of roots of the equation : 2x2 - 2x + 1 = 0

3. What is the nature of roots of the equation : 2x2 - 2x + 1 = 0

Correct Answer Option A

Detailed Solution

Solution Details

Given 2x2 - 2x + 1 = 0

• 2x2 - 2x + 1 = 0 a = 2, b = - 2, c = 1

• Δ = b2 - 4ac = ( - 2 )2 - 4 ( 2 ) ( 1 ) = - 4

• Δ < 0

∴ The roots are Non-Real

4. For which values of k will the equation x2 + x = k have no real roots ?

4. For which values of k will the equation x2 + x = k have no real roots ?

4. For which values of k will the equation x2 + x = k have no real roots ?

Correct Answer Option A

Detailed Solution

Solution Details

Given x2 + x = k

• x2 + x - k = 0 a = 1, b = 1, c = - k

• Δ < 0 b2 - 4ac < 0 ( 1 )2 - 4 ( 1 ) ( - k ) < 0 1 + 4k < 0 4k < - 1 ∴ k < - 1 4

5. The roots of a quadratic equation are : x = 3 ± – k – 4 2 For which values of k are the roots real

5. The roots of a quadratic equation are : x = 3 ± – k – 4 2 For which values of k are the roots real

5. The roots of a quadratic equation are : x = 3 ± – k – 4 2 For which values of k are the roots real

Correct Answer Option C

Detailed Solution

Solution Details

Given x = 3 ± – k – 4 2

• x = 3 ± – k – 4 2

• - k - 4 ≥ 0

• - k ≥ 4

∴ k ≤ - 4

1. What is the nature of roots of the equation : x² + 8x + 16 = 0

1. What is the nature of roots of the equation : x² + 8x + 16 = 0

1. What is the nature of roots of the equation :

x² + 8x + 16 = 0

2. What is the nature of roots of the equation : x² - 5x + 3 = 0

2. What is the nature of roots of the equation : x² - 5x + 3 = 0

2. What is the nature of roots of the equation :

x² - 5x + 3 = 0

3. What is the nature of roots of the equation : 2x² - 2x + 1 = 0

3. What is the nature of roots of the equation : 2x² - 2x + 1 = 0

3. What is the nature of roots of the equation :

2x² - 2x + 1 = 0

4. For which values of k will the equation x² + x = k have no real roots ?

4. For which values of k will the equation x² + x = k have no real roots ?

4. For which values of k will the equation

x² + x = k

have no real roots ?

5. The roots of a quadratic equation are : x = $\frac{3 ± \sqrt[]{– k – 4}}{2}$

For which values of k are the roots real

5. The roots of a quadratic equation are : x = $\frac{3 ± \sqrt[]{– k – 4}}{2}$

For which values of k are the roots real

5. The roots of a quadratic equation are :

x = $\frac{3 ± \sqrt[]{– k – 4}}{2}$

For which values of k are the roots real

1. What is the nature of roots of the equation : x² + 8x + 16 = 0

1. What is the nature of roots of the equation : x² + 8x + 16 = 0

1. What is the nature of roots of the equation :

x² + 8x + 16 = 0

Correct Answer
Option B

Given x² + 8x + 16 = 0

• x² + 8x + 16 = 0

a = 1, b = 8, c = 16

• Δ = b² - 4ac

= 8² - 4 ( 1 ) ( 16 ) = 0

2. What is the nature of roots of the equation : x² - 5x + 3 = 0

2. What is the nature of roots of the equation : x² - 5x + 3 = 0

2. What is the nature of roots of the equation :

x² - 5x + 3 = 0

Correct Answer
Option C

Given x² - 5x + 3 = 0

• x² - 5x + 3 = 0

a = 1, b = - 5, c = 3

• Δ = b² - 4ac

= ( - 5 )² - 4 ( 1 ) ( 3 ) = 13

3. What is the nature of roots of the equation : 2x² - 2x + 1 = 0

3. What is the nature of roots of the equation : 2x² - 2x + 1 = 0

3. What is the nature of roots of the equation :

2x² - 2x + 1 = 0

Correct Answer
Option A

Given 2x² - 2x + 1 = 0

• 2x² - 2x + 1 = 0

a = 2, b = - 2, c = 1

• Δ = b² - 4ac

= ( - 2 )² - 4 ( 2 ) ( 1 ) = - 4

4. For which values of k will the equation x² + x = k have no real roots ?

4. For which values of k will the equation x² + x = k have no real roots ?

4. For which values of k will the equation

x² + x = k

have no real roots ?

Correct Answer
Option A

Given x² + x = k

• x² + x - k = 0

a = 1, b = 1, c = - k

• Δ < 0

b² - 4ac < 0

( 1 )² - 4 ( 1 ) ( - k ) < 0

1 + 4k < 0

4k < - 1

∴ k < - $\frac{1}{4}$

5. The roots of a quadratic equation are : x = $\frac{3 ± \sqrt[]{– k – 4}}{2}$

For which values of k are the roots real

5. The roots of a quadratic equation are : x = $\frac{3 ± \sqrt[]{– k – 4}}{2}$

For which values of k are the roots real

5. The roots of a quadratic equation are :

x = $\frac{3 ± \sqrt[]{– k – 4}}{2}$

For which values of k are the roots real

Correct Answer
Option C

Given x = $\frac{3 ± \sqrt[]{– k – 4}}{2}$

• x = $\frac{3 ± \sqrt[]{– k – 4}}{2}$