Question

If $\alpha ,\beta$ are the zeroes of the polynomials $2y^2+7y+5$, then find the value of $\alpha +\beta +\alpha \beta .$

Answer 1

Given polynomial $2y^2+7y+5$

Here $a=2,b=7,c=5$

$\alpha ,\beta$ are two zeroes

So, sum of the zeroes $=\alpha +\beta =-\frac{b}{a}$

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

Product of the zeroes $=\alpha \beta =\frac{c}{a}$

$=\frac{5}{2}$

Now just put the values

$\alpha +\beta +\alpha \beta =(\alpha +\beta )+\alpha \beta$

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

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

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

$=-1$

$\therefore$ So, the required answer is $-1$.