# Find a quadratic polynomial whose zeros are 2 and −5.

Question:

Find a quadratic polynomial whose zeros are 2 and −5.

Solution:

It is given that the two roots of the polynomial are 2 and −5.

Let $\alpha=2$ and $\beta=-5$

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

Product of the zeroes, $\alpha \beta=2 \times-5=-10$

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

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

$=x^{2}+3 x-10$