Question

If $\alpha ,\beta$ be the zeros of the quadratic polynomial $2-3x-x^2$, then $\alpha +\beta =$

• A. $2$
• B. $9$
• C. $1$
• D. none of these

Answer 1

The correct option is D none of these

If $\alpha$ and $\beta$ are the zeros of the polynomial then
$(x-\alpha )(x-\beta )$ are the factors of the polynomial
Thus, $(x-\alpha )(x-\beta )$ is the polynomial.
So, the polynomial $=x^2-\alpha x-\beta x+\alpha \beta$
$=x^2-(\alpha +\beta )x+\alpha \beta ....\left(i\right)$
Now,the quadratic polynomial is
$2-3x-x^2=$ $x^2+3x-2....\left(ii\right)$

Now, comparing equation (i) and (ii),we get,
$-(\alpha +\beta )=3$
$\alpha +\beta =-3$