Question

For equation $2x^2+16x+3k=0$ sum of the squares of roots is $10$, then $k$ is

Answer 1

Finding the value of $k$ :

Given that $2x^2+16x+3k=0$

Sum of squares of roots is $10$

Let $\alpha ,\beta$ be the roots of given expression

$$\begin{gathered} ɑ+\beta =–8, \\ ɑ\beta =3k/2 \\ {ɑ}^2+{\beta }^2=10 \\ {(ɑ+\beta )}^2–2ɑ\beta =10 \\ 64–3k=10 \\ k=18 \end{gathered}$$

Hence the value of $k$ is $18$.