If the equation $16 x^{2} + 6 k x + 4 = 0$ has equal roots, then the value of $k$ is

\pm 8

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\pm \frac{8}{3}

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\pm \frac{3}{8}

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Solution

The correct option is B $\pm \frac{8}{3}$
$16 x^{2} + 6 k x + 4 = 0$ has equal roots
Therefore, $D = 0$
$\Rightarrow D = b^{2} - 4 a c$
$\Rightarrow (6 k)^{2} - 4 (16) (4) = 0$
$\Rightarrow 36 k^{2} - 256 = 0$
$\Rightarrow k^{2} = \frac{256}{36} = \frac{64}{9}$
$\Rightarrow k = \pm \frac{8}{3}$

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If 2 is a root of the quadratic equation $3 x^{2} + p x - 8 = 0$ and the quadratic eqation $4 x^{2} - 2 p x + k = 0$ has equal roots, find the value of k.

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Q. Find k if one root of the equation

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If the equation 16x2+6kx+4=0 has equal roots, then the value of k is

The correct option is B ±8316x2+6kx+4=0 has equal roots Therefore, D=0⇒D=b2−4ac⇒(6k)2−4(16)(4)=0⇒36k2−256=0⇒k2=25636=649⇒k=±83

If the equation $16 x^{2} + 6 k x + 4 = 0$ has equal roots, then the value of $k$ is

The correct option is B $\pm \frac{8}{3}$
$16 x^{2} + 6 k x + 4 = 0$ has equal roots
Therefore, $D = 0$
$\Rightarrow D = b^{2} - 4 a c$
$\Rightarrow (6 k)^{2} - 4 (16) (4) = 0$
$\Rightarrow 36 k^{2} - 256 = 0$
$\Rightarrow k^{2} = \frac{256}{36} = \frac{64}{9}$
$\Rightarrow k = \pm \frac{8}{3}$