  # Find a quadratic polynomial whose zeroes are -3 and 4.

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Updated on: September 25th, 2023 A quadratic polynomial whose zeroes are -3 and 4 is x2 – x -12. A quadratic polynomial is a polynomial of degree 2. It is a polynomial expression that can be written in the form:

f(x) = (x – α)(x – β)

Expanding this expression, we get:

f(x) = x2 – (α + β)x + αβ

The sum of the zeroes is given by α + β, and the product of the zeroes is given by αβ. These values can be used to construct the quadratic polynomial in the form mentioned above.

Table of content To find a quadratic polynomial with zeroes at -3 and 4, we can use the fact that the product of the roots of a quadratic equation is equal to the constant term divided by the coefficient of the quadratic term.

We know that a quadratic polynomial is of 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

Solution

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. Quadratic polynomials are expressed as –

f(x) = x2 – (α + β)x + αβ

The term x2 represents the coefficient of the quadratic term. The term -(α + β)x represents the coefficient of the linear term. The term αβ represents the constant term.

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