Question

Find the values of ${}^{\prime }{k}^{\prime }$ in $2x^2+kx+3=0$, so that they have two equal roots?

Answer 1

Given equation is $2x^2+kx+3=0$

On comparing the given equation with standard equation $a{x}^2+bx+c=0$, we have

$a=2,b=k$ and $c=3$

It is given that the given equation has equal roots.

We know that for equal roots Discriminant would be equal to zero.

So, its Discriminant, $D=b^2-4ac=0$

$\Rightarrow k^2-4\left(2\right)\left(3\right)=0$

$\Rightarrow k^2=24$

$\Rightarrow k=\pm \sqrt{24}$

so, there will be two values of $k$ i.e. $+\sqrt{24}$ and $-\sqrt{24}$ for which the given equation has equal roots.