Question

$\alpha$ and $\frac{1}{\alpha }$ are zeroes of polynomial $4x^2-2x+k+7$. Find the value of $k$.

Answer 1

According to the problem,

$\alpha ,\frac{1}{\alpha }$ are the roots of the equation $4x^2-2x+k+7=0$.

Now by the relation between the roots and co-efficients we get,

$\alpha .\frac{1}{\alpha }=\frac{k+7}{4}\dots (productofroots=\frac{c}{a})$

or, $4=k+7$

or, $k=-3$.