Question

If $\frac{-1}{2}$ is one root of quadratic equation $2x^2+kx+1=0$ , Find K.

Answer 1

Given $2x^2+kx+1=0$---(1)

we know that

if $\alpha ,\beta$ be roots of eq (1) then

$\alpha +\beta =\frac{-k}{\alpha }$ and $\alpha \beta =\frac{1}{2}$

and$[\alpha =\frac{-1}{2}]$ Given

then$\beta =\frac{\frac{1}{2}}{\frac{1}{2}}=-1$

and $\alpha +\beta =\frac{-k}{2}=-1\frac{-1}{2}$

$\frac{-k}{2}=\frac{-3}{2}$ [k=3]

Hence volume of k is 3.