# A quadratic polynomial whose zeros are 5 and −3, is

Question:

A quadratic polynomial whose zeros are 5 and −3, is

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

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

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

(d) none of these

Solution:

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

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

Let $\alpha=5$ and $\beta$

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

Also, 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 $x^{2}-2 x-15$.