Find a quadratic polynomial whose zeroes are -4 and 2

By Shivank Goel|Updated : August 2nd, 2022

We know that a quadratic polynomial is of the form f(x) = ax2+bx+c and a ≠ 0

A quadratic polynomial in terms of zeroes (α,β) is written as

x2 -(sum of the zeroes) x + (product of the zeroes)

So we get

f(x) = x2 -(α +β) x +αβ

It is asked to find a quadratic polynomial whose zeroes are -4 and 2.

Zeroes of a quadratic polynomial are -4 and 2

Consider α = -4 and β= 2

Now substitute α = -4 and β= 2 in f(x) = x2 -(α +β) x +αβ

f(x) = x2 - ( -4 + 2) x +(-4)(2)

We get

f(x) = x2 - 2x -8

Therefore, when asked to find a quadratic polynomial whose zeroes are -4 and 2, then the answer will be a quadratic polynomial whose zeroes are -4 and 2 is x2 - 2x - 8.

Summary:

Find a quadratic polynomial whose zeroes are -4 and 2.

A quadratic polynomial whose zeroes are -4 and 2 is x2 - 2x - 8.

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