Question

A quadratic polynomial whose zeros are $5$ and $-3,$ is

(a) $x^2+2x-15$

(b) $x^2-2x+15$

(c) $x^2-2x-15$

(d) none of these

Answer 1

The correct option is (c): $x^2-2x-15$

Here, the zeroes are $5$ and $-3.$

Let $\alpha =5$ and $\beta =-3$ [$\alpha$ and $\beta$ are the zeros of the polynomial]

So, sum of the zeroes, $\alpha +\beta =5+(-3)=2$

Also, the product of the zeroes, $\alpha \beta =5\times (-3)=-15$

The polynomial will be $x^2-(\alpha +\beta )x+\alpha \beta .$

$\therefore$ The required polynomial is $x^2-2x-15.$