Question

Assertion: The equation x² + 4x − 19 = 0 has both real roots.

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

पर्याय

• 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):

x² + 4x − 19 = 0

Δ = b2 − 4ac

= 42 − 4(1) (−19)

= 16 + 76

= 92

Since Δ > 0, the equation has two real (distinct) roots.

Assertion (A) is true.

Reason (R):

This statement is incorrect because:

b² − 4ac = 0 → equal real roots

b² − 4ac > 0 → two real and distinct roots

Reason (R) is false.