# Find a Quadratic Polynomial Whose Zeroes are -4 and 2

A quadratic polynomial is of the form f(x) = ax^{2}+bx+c and a ≠ 0

## Answer: x^{2} + 2x - 8 is the Quadratic Polynomial Whose zeroes are -4 and 2

Let us see, how to solve.

## Explanation:

A quadratic polynomial in terms of the zeroes (α,β) is given by

x^{2} - (sum of the zeroes) x + (product of the zeroes)

i.e,

f(x) = x^{2} - (α +β) x +αβ

Now,

Given that zeroes of a quadratic polynomial are -4 and 2

let α = -4 and β= 2

Therefore, substituting the value α = -4 and β= 2 we get

f(x) = x^{2} - (α + β) x + αβ

= x^{2} - ( -4 + 2) x +(-4)(2)

= x^{2} + 2x - 8

### Thus, x^{2} + 2x - 8 is the quadratic polynomial whose zeroes are -4 and 2.

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