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For what values of ‘k’ the quadratic equation $2 x ² + k x + 3 = 0$ have two equal roots?

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k = ± 26

k = 3

k=5

k = ± 36

answer is A.

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Detailed Solution

Given equation is

2 x ² + k x + 3 = 0

.
We know that the standard form of a quadratic equation is

a x 2 + b x + c = 0, a ≠ 0

, for which the roots are

x = − b ± b 2 − 4 a c 2 a

.
Here, a = 2, b = k, c = 3.
Now it is given that the equation has two equal roots. So,

b 2 − 4 a c = 0

⇒ (k) 2 − 4 (2) (3) = 0

⇒ k 2 − 24 = 0

⇒ k = ± 24

⇒ k = ± 26

The value of k for which the given quadratic equation

have two equal roots is

k = ± 26

.
Therefore, the correct option is 1.

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