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Assertion & Reason Test: Quadratic Equations - 2 - Class 10 MCQ


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10 Questions MCQ Test Online MCQ Tests for Class 10 - Assertion & Reason Test: Quadratic Equations - 2

Assertion & Reason Test: Quadratic Equations - 2 for Class 10 2024 is part of Online MCQ Tests for Class 10 preparation. The Assertion & Reason Test: Quadratic Equations - 2 questions and answers have been prepared according to the Class 10 exam syllabus.The Assertion & Reason Test: Quadratic Equations - 2 MCQs are made for Class 10 2024 Exam. Find important definitions, questions, notes, meanings, examples, exercises, MCQs and online tests for Assertion & Reason Test: Quadratic Equations - 2 below.
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Assertion & Reason Test: Quadratic Equations - 2 - Question 1

DIRECTION : In the following questions, a statement of assertion (A) is followed by a statement of reason (R). Mark the correct choice as:

Assertion : The values of x are a for a quadratic equation 2x2 +ax- a2 =0 .

Reason : For quadratic equation ax2 + bx+ c = 0

Detailed Solution for Assertion & Reason Test: Quadratic Equations - 2 - Question 1
2x2 +ax- a2 = 0

So, A is incorrect but R is correct.

Assertion & Reason Test: Quadratic Equations - 2 - Question 2

DIRECTION : In the following questions, a statement of assertion (A) is followed by a statement of reason (R). Mark the correct choice as:

Assertion : The value of k = 2 , if one root of the quadratic equation 6x2 -x- k = 0 is ⅔

Reason : The quadratic equation ax2 + bx + c = 0, a ≠ 0 a has two roots.

Detailed Solution for Assertion & Reason Test: Quadratic Equations - 2 - Question 2

As one root is x =

k = 2

So, both A and R are correct but R does not explain A.

Assertion & Reason Test: Quadratic Equations - 2 - Question 3

DIRECTION : In the following questions, a statement of assertion (A) is followed by a statement of reason (R). Mark the correct choice as:

Assertion : If roots of the equation x2 - bx + c = 0 are two consecutive integers, then b2 - 4c =1

Reason : If a, b, c are odd integer then the roots of the equation 4abc x2 + (b2 - 4ac)x - b = 0 are real and distinct.

Detailed Solution for Assertion & Reason Test: Quadratic Equations - 2 - Question 3

Assertion : Given equation

x2 - bx + c = 0

Let α,β be two roots such that

|α, - β|2 = 1

(α + β)2 - 4αβ = 1

b2 - 4c = 1

Reason : Given equation

4abc x2 + (b2- 4ac) x - b = 0

D = (b2 - 4ac)+ 16ab2 c

D = (b2 - 4ac)2 > 0

Hence roots are real and unequal.

Assertion & Reason Test: Quadratic Equations - 2 - Question 4

DIRECTION : In the following questions, a statement of assertion (A) is followed by a statement of reason (R). Mark the correct choice as:

Assertion : A quadratic equation ax2 + bx + c = 0 , has two distinct real roots, if b2 - 4ac >0 .

Reason : A quadratic equation can never be solved by using method of completing the squares.

Detailed Solution for Assertion & Reason Test: Quadratic Equations - 2 - Question 4
If a = 0, it becomes linear equation.

If b2 − 4ac = 0, then there will be real and equal roots.

If b2 − 4ac < 0, then the roots will be unreal.

Only if b2 − 4ac > 0, we will get two real distinct roots.

Assertion & Reason Test: Quadratic Equations - 2 - Question 5

DIRECTION : In the following questions, a statement of assertion (A) is followed by a statement of reason (R). Mark the correct choice as:

Assertion : 4x2 -12x+9 =0 has repeated roots.

Reason : The quadratic equation ax2 + bx + c = 0 have repeated roots if discriminant D > 0 .

Detailed Solution for Assertion & Reason Test: Quadratic Equations - 2 - Question 5
Assertion 4x2 - 12x + 9 = 0

D = b2 - 4ac

= (- 12)2 - 4(4)(9)

= 144 - 144 = 0

Roots are repeated.

Assertion & Reason Test: Quadratic Equations - 2 - Question 6

DIRECTION : In the following questions, a statement of assertion (A) is followed by a statement of reason (R). Mark the correct choice as:

Assertion : (2x - l)2 - 4x2 + 5 = 0 is not a quadratic equation.

Reason : x = 0, 3 are the roots of the equation 2x2 -60x = 0.

Detailed Solution for Assertion & Reason Test: Quadratic Equations - 2 - Question 6
Assertion and Reason both are true statements. But Reason is not the correct explanation.

Assertion (2x - 1)2 - 4x2 + 5 = 0

- 4x + 6 = 0

Reason 2X2 - 6x = 0

2x(x - 3) = 0

x = 0

and x = 3

Assertion & Reason Test: Quadratic Equations - 2 - Question 7

DIRECTION : In the following questions, a statement of assertion (A) is followed by a statement of reason (R). Mark the correct choice as:

Assertion : The equation 8x2 + 23kx+0 = has equal roots then the value of k is

Reason : The equation ax2 + bx+ c = 0 has equal roots if D =b2 - 4ac =0

Detailed Solution for Assertion & Reason Test: Quadratic Equations - 2 - Question 7

8x2 + 3kx + 2 = 0

Discriminant, D = b2 - 4ac

D = (3k)2 - 4 x 8 x 2 = 9k2 - 64

For equal roots, D = 0

9k2 - 64 = 0

9k2 = 64

So, A and R both are correct and R explains A.

Assertion & Reason Test: Quadratic Equations - 2 - Question 8

DIRECTION : In the following questions, a statement of assertion (A) is followed by a statement of reason (R). Mark the correct choice as:

Assertion : The roots of the quadratic equation x2 + 2x+2 = 0 are imaginary.

Reason : If discriminant D =b2 - 4ac <0 then the roots of quadratic equation ax2 + bx+ c = 0 are imaginary.

Detailed Solution for Assertion & Reason Test: Quadratic Equations - 2 - Question 8
x2 + 2x + 2 = 0

Discriminant, D = b2 - 4ac

= (2)2 - 4 x 1 x 2

= 4 - 8 = - < 04

Roots are imaginary.

So, both A and R are correct and R explains A.

Assertion & Reason Test: Quadratic Equations - 2 - Question 9

DIRECTION : In the following questions, a statement of assertion (A) is followed by a statement of reason (R). Mark the correct choice as:

Assertion : The equation 9x2 + 34kx + 4 = 0 has equal roots for k = + 4 .

Reason : If discriminant ‘D’ of a quadratic equation is equal to zero then the roots of equation are real and equal.

Detailed Solution for Assertion & Reason Test: Quadratic Equations - 2 - Question 9

Assertion 9x2 + 43kx + 4 = 0

D = b2 - 4ac

= (3k)2 - 4(9)(4)

= 9k2 - 144

For equal roots D = 0

9k2 = 144

k = ± 4

Assertion & Reason Test: Quadratic Equations - 2 - Question 10

DIRECTION : In the following questions, a statement of assertion (A) is followed by a statement of reason (R). Mark the correct choice as:

Assertion : Sum and product of roots of 2x2 -35x+0 = are and respectively.

Reason : If a and b are the roots of ax2 + bx + c = 0 , a ≠ 0 , then sum of roots = α +β = and product of roots

Detailed Solution for Assertion & Reason Test: Quadratic Equations - 2 - Question 10
Assertion and Reason both are correct and Reason is correct explanation.

Assertion 2x2 - 53x+ = 0

and

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