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

By BYJU'S Exam Prep

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

1. Quadratic Polynomial
2. Find a quadratic polynomial whose zeroes are -3 and 4.

Quadratic Polynomial

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