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