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

compare the equation with $a{y}^2+by+c$

$a=2$

$b=7$

$c=5$

sum of the roots,

$\alpha +\beta =\frac{-b}{a}$ $=\frac{-7}{2}$

product of the roots,

$\alpha \beta =\frac{c}{a}$ $=\frac{5}{2}$

now,

$\alpha +\beta +\alpha \beta =\frac{5}{2}-\frac{7}{2}$ $=-1$