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If the equation $4 x^{2} - 3 kx + 1 = 0$ has equal roots then k =?

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\pm \frac{2}{3}

\pm \frac{1}{3}

\pm \frac{3}{4}

\pm \frac{4}{3}

answer is D.

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Detailed Solution

Given quadratic equation is,

4 x^{2} - 3 kx + 1 = 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

4 x^{2} - 3 kx + 1 = 0

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

a = 4, b = 3 k, c = 1

.
Then,

⟹ b^{2} - 4 ac = 0

⟹ {(3 k)}^{2} - 4 \times 4 \times 1 = 0

⟹ 9 k^{2} - 16 = 0

⟹ 9 k^{2} = 16

⟹ k^{2} = \frac{16}{9}

⟹ k = \sqrt{\frac{16}{9}}

∴ k = \pm \frac{4}{3}

∴

If the equation

4 x^{2} - 3 kx + 1 = 0

has equal roots then

k = \pm \frac{4}{3}

Hence, the correct option is 4.

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