Chapter 4 Quadratic Equations Assertation & Reasoning Questions Class 10th

Direction: In the following questions, a statement of Assertion (A) is followed by a statement of Reason (R). Mark the correct choice as:
(a) Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A).
(b) Both Assertion (A) and Reason (R) are true but Reason (R) is not the correct explanation of
Assertion (A).
(c) Assertion (A) is true but Reason (R) is false.
(d) Assertion (A) is false but Reason (R) is true

Q.1. Assertion: If one root of the quadratic equation 6x² – x – k = 0 is 2/3, then the value of k is 2.
Reason: The quadratic equation ax² + bx + c = 0, a ≠ 0 has almost two roots.

Q.2. Assertion: (2x – 1)² – 4x² + 5 = 0 is not a quadratic equation.
Reason: An equation of the form ax² + bx + c = 0, a ≠ 0, where a, b, c ∈ R is called a quadratic equation.

Answer:

Q.3. 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.

Answer:

Q.4. Assertion: 3x² – 6x + 3 = 0 has repeated roots.
Reason: The quadratic equation ax² + bx + c = 0 have repeated roots if discriminant D > 0.

Answer:

Q5. Assertion: x²+x³+2 has no quadratic equation.

     Reason: it has degree 3

a.) Both Assertion and Reason are correct and Reason is the correct explanation for Assertion

b.) Both Assertion and Reason are correct and Reason is not the correct explanation for Assertion.

c.) assertion is true but the reason is false.

d.) both assertion and reason are false.

Ans: a) Both Assertion and Reason are correct and Reason is the correct explanation for Assertion

Q6. Assertion: If one root of the quadratic equation 2x² + kx – 6 = 0 is 2, the value of k is -1

Reason: x = 2 is a root of the equation 2x² + kx -6 = 0

∴ 2(2)² +k(2) – 6 = 0

⇒ 8 + 2k – 6 = 0

⇒ 2k = -2

∴ k = -1

a.) Both Assertion and Reason are correct and Reason is the correct explanation for Assertion

b.) Both Assertion and Reason are correct and Reason is not the correct explanation for Assertion.

c.) assertion is true but the reason is false.

d.) both assertion and reason are false.

Ans: a) Both Assertion and Reason are correct and Reason is the correct explanation for Assertion

Q7. Assertion: The roots of the equation 7x² + x – 1 = 0 are real and distinct

     Reason : if b²-4ac >0 then roots are real and distinct.

a.) Both Assertion and Reason are correct and Reason is the correct explanation for Assertion

b.) Both Assertion and Reason are correct and Reason is not the correct explanation for Assertion.

c.) assertion is true but the reason is false.

d.) both assertion and reason are false.

Ans: a) Both Assertion and Reason are correct and Reason is the correct explanation for Assertion

Q8.Assertion: Every quadratic equation has at most two root

Reason: Every quadratic equation has atleast one real root.

a.) Both Assertion and Reason are correct and Reason is the correct explanation for Assertion

b.) Both Assertion and Reason are correct and Reason is not the correct explanation for Assertion.

c.) assertion is true but the reason is false.

d.) both assertion and reason are false.

Ans: c) Assertion  is  correct but reason is false.

Q9. Assertion: 4x² – 12x+ 9= 0 has repeated roots.

Reason : The quadratic equation ax²+ bx² + c = 0 have repeated roots if discriminant D > 0.

a.) Both Assertion and Reason are correct and Reason is the correct explanation for Assertion

b.) Both Assertion and Reason are correct and Reason is not the correct explanation for Assertion.

c.) assertion is true but the reason is false.

d.) both assertion and reason are false.

Ans: c) Assertion  is  correct but reason is false

Q10. Assertion: Any equation of the form ax²+ bx+c = 0 where a not equal to  0, is called a quadratic equation

Reason: The equation x² +3x+1=(x-2)² is a quadratic equation .

a.) Both Assertion and Reason are correct and Reason is the correct explanation for Assertion

b.) Both Assertion and Reason are correct and Reason is not the correct explanation for Assertion.

c.) assertion is true but the reason is false.

d.) both assertion and reason are false.

Ans: c) Assertion  is  correct but reason is false.