The sum and product of the zeros of a quadratic polynomial are 3 and −10 respectively.
Question:

The sum and product of the zeros of a quadratic polynomial are 3 and −10 respectively. The quadratic polynomial is

(a) $x^{2}-3 x+10$

(b) $x^{2}+3 x-10$

(c) $x^{2}-3 x-10$

(d) $x^{2}+3 x+10$

Solution:

(c) $x^{2}-3 x-10$

Given: Sum of zeroes, $\alpha+\beta=3$

Also, product of zeroes, $\alpha \beta=-10$

$\therefore$ Required polynomial $=x^{2}-(\alpha+\beta)+\alpha \beta=x^{2}-3 x-10$