Question

Find the value of K for the quadratic equation $2x^2+kx+3=0$ , so that they have two equal roots.

Answer 1

Consider the given equation.

$2x^2+kx+3=0$

Since, the roots are equal.

$\alpha +\alpha =\frac{-K}{2}$

$2\alpha =\frac{-K}{2}$

$\alpha =\frac{-K}{4}$

And $\alpha \times \alpha =\frac{3}{2}$

$(\alpha {)}^2=\frac{3}{2}$

Therefore,

$(\frac{-K}{4}{)}^2=\frac{3}{2}$

$\frac{K^2}{16}=\frac{3}{2}$

$K^2=\frac{3\times 16}{2}$

$K^2=24$

$K=2\sqrt{6}$

Hence, this is the answer.