Question

How to find a quadratic polynomial from given zeros?

Answer 1

Hi friend!!

Let à and ß are the zeroes of the quadratic polynomial.

Here are two methods:-

Method - 1:-
Find sum and product of zeroes!

Sum of zeroes = (à+ß)
Product of zeroes = àß

The quadratic polynomial which has two zeroes is in the form of
x² - (à+ß)x + as

Thus,we can find!

Method-2:-

We should know the relation between zeroes and coefficients.

» Sum of zeroes = -x coefficient/x² coefficient
à+ß = -x coefficient/x² coefficient

» Product of zeroes = constant/x² coefficient
àß = constant/x² coefficient

By substituting the coefficients of x²,x and constant,we can find the quadratic polynomial.