Question

Find a quadratic polynomial whose zeros are $7$ and $-5$

Answer 1

Solution:-

As the zeroes are given, i.e., 7 and -5.

$\therefore$ Sum of roots $=7+(-5)=7-5=2$

Product of roots $=7\times (-5)=-35$

As we know that, a quadratic polynomial whose xeroes are given can be represented as-

$x^2-\left(\text{sum of roots}\right)x+\text{product of roots}=0$

$\Rightarrow x^2-\left(2\right)x+(-35)=0$

$\Rightarrow x^2-2x-35=0$

Hence, the polynomial is $x^2-2x-35=0$.