Question

If x=1/2 is a solution of the quadratic equation 9x^2+3kx+k =0,find the value of k.

Answer 1

Answer.

9x² + 3kx + k = 0

Since,

$x = \frac{1}{2} \: is \: a \: root \: of \: the \: equation$

So,

$9 {( \frac{1}{2} )}^{2} + 3k( \frac{1}{2} ) + k = 0$

$⇒ \: \frac{9}{4} + ( \frac{3}{2} )k + k = 0$

$⇒ \: \frac{9 + 6k + 9k}{4} = 0$

$⇒ \: 15k \: + 9 = 0$

$⇒ \: k \: = \frac{ - 9}{15} = \frac{ - 3}{5}$

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