Find a quadratic polynomial whose zeroes are -3 and 4

By Shivank Goel|Updated : August 1st, 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

So we are asked to Find a quadratic polynomial whose zeroes are -3 and 4; it is given that

Zeroes of a quadratic polynomial are -3 and 4

Consider α = -3 and β= 4

Now substitute α = -3 and β= 4 in f(x) = x2 -(α +β) x +αβ

f(x) = x2 - ( -3 + 4) x +(-3)(4)

We get

f(x) = x2 - x -12

So if you are asked to Find a quadratic polynomial whose zeroes are -3 and 4, then your answer will be a quadratic polynomial whose zeroes are -3 and 4 is x2 - x -12.

Summary:

Find a quadratic polynomial whose zeroes are -3 and 4

A quadratic polynomial whose zeroes are -3 and 4 is x2 - x -12.

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