Question

Find the value of$k$in $2x^2+kx+3=0$so that they have two equal roots.

Answer 1

Find the value

It is given that the equation $2x^2+kx+3=0$ has two equal roots.

We know that if two roots of the equation $a{x}^2+bx+c=0$ are equal then $b^2-4ac=0$

Now comparing with the standard form we have $b=k,a=2$ and $c=3$

$$\begin{gathered} \therefore b^2-4ac=0 \\ \Rightarrow k^2-4·2·3=0 \\ \Rightarrow k^2-24=0 \\ \Rightarrow k^2=24 \\ \Rightarrow k=\pm \sqrt{24}=\pm 2\sqrt{6} \end{gathered}$$

Hence the value of $k$ is $\pm 2\sqrt{6}$