Question

If $\alpha$ and $\beta$ are the zeros of the polynomial $2x^2+7x+5$, write the value of $\alpha +\beta +\alpha \beta .$

Answer 1

We have $2x^2+7x+5=0$

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

$\alpha$ and $\beta$ are the zeros

So sum of the zeroes

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

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

Now just put the values

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

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

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

So required answer is -1

$\alpha +\beta +\alpha \beta =-1$