Question

Find a quadratic polynomial whose zeros are 5 and -5.

Answer 1

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

Sum of zeros $=5-5=0$

Products of zeros $=5\times -5=-25$

Hence, the quadratic polynomial is $=k{x}^2+(\text{sum of zeros)}x+\text{product of zeros}$

Putting the values in quadratic polynomial $=k{x}^2-0+(-25)$.

Hence, the quadratic polynomial is ${kx}^2-25$, where k is constant.