Question

K for which the quadratic equation 9 x square - 3 k x + K equals to zero has equal roots
​

Answer 1

$\huge{\tt{\underline{\underline{AnSwEr}}}}$

It is given that quadratic equation has equal roots, it means that $\sf\ D = 0$

Now ; the formula used is

$\large{\boxed{\boxed{\tt{\pink{D \: = \: b^2 \: - \: 4ac}}}}}$

$\rule{300}{2}$

Equation is;

$\tt\ 9x^2 \: - \: 3kx \: + \: k \:$

Here,

★ a = 9

★b = -3k

★ c= k

$\rule{300}{2}$

$\tt\implies\ (-3k) ^2 \: - \: 4 \times\ 9 \times\ k \: = \: O \\ \\ \tt\implies\ 9k^2 \: - \: 36k = 0 \\ \\ \tt\implies\ k \: = \: \frac{36k}{9k} \: = \: 4$