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If the equation $9 x^{2} + 6 kx + 4 = 0$ has equal roots then k=?

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\pm 1

\pm 2

\pm 5

\pm 3

answer is C.

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Detailed Solution

Given quadratic equation is,

9 x^{2} + 6 kx + 4 = 0

.
We know that, a quadratic equation

a x^{2} + bx + c = 0

has two equal roots if

b^{2} - 4 ac = 0

.
After comparing the given equation

9 x^{2} + 6 kx + 4 = 0

with the standard form of the quadratic equation, we get,

a = 9, b = 6 k, c = 4

.
Then,

{⟹ b}^{2} - 4 ac = 0

⟹ {(6 k)}^{2} - 4 \times 9 \times 4 = 0

⟹ 36 k^{2} - 144 = 0

⟹ 36 k^{2} = 144

⟹ k^{2} = \frac{144}{36}

⟹ k^{2} = \frac{12}{3}

⟹ k^{2} = 2

∴ k = \pm 2

∴

If the equation

9 x^{2} + 6 kx + 4 = 0

has equal roots then

k = \pm 2

Hence, the correct option is 3.

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