Assertion (A): The quadratic equation

Question

Assertion (A): The quadratic equation $9 x ² + 3 k x + 4 = 0 h a s e q u a l r o o t s f o r k = \pm 4 .$

Reason (R): If the discriminant of a quadratic equation is equal to zero, then the roots of the equation are real and equal.

Smart Achievers · Accepted Answer

(1)

We have the quadratic equation $9 x ² + 3 k x + 4 = 0 .$
For roots to be equal, D = 0.

⇒ $(3 k) ² - 4 \times 9 \times 4 = 0 \Rightarrow 9 k ² - 144 = 0$

$\Rightarrow 9 k ² = 144 \Rightarrow k ² = 16$

$\Rightarrow k = \pm 4$ .

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

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