Question

If $\alpha$ and $\beta$ are the zeroes of the polynomial $2y^2+7y+5$, write the values of $\alpha +\beta +\alpha \beta$.

Answer 1

$\alpha \&\beta$ax zeros of $2y^2+2y+5$

Now sum of roots $=\alpha +\beta =-\frac{7}{2}$

Product $=\alpha \beta =\frac{5}{2}$

$\alpha +\beta +\alpha \beta$

$=-\frac{7}{2}+\frac{5}{2}$

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