Question

Assertion: The equation 9x² − 6x + 1 = 0 has equal roots.

Reason: The equation ax² + bx + c = 0, a ≠ 0 has equal roots if b² − 4ac > 0.

Options

• Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A).

• Both Assertion (A) and Reason (R) are true but Reason (R) is not the correct explanation of Assertion (A).

• Assertion (A) is true but Reason (R) is false.

• Assertion (A) is false but Reason (R) is true.

Answer 1

Assertion (A) is true but Reason (R) is false.

Explanation:

Assertion (A):

9x² − 6x + 1 = 0

Δ = b² − 4ac

= (−6)² − 4(9) (1)

= 36 − 36

= 0

Since the discriminant is 0, the equation has equal roots.

Assertion (A) is true.

Reason (R):

A quadratic equation has:

equal roots if b² − 4ac = 0

distinct real roots if b2 − 4ac > 0

Reason (R) is false.