Find a quadratic polynomial, the sum and product of whose zeroes are – 3 and 2 respectively.

By BYJU'S Exam Prep

Updated on: September 25th, 2023

The quadratic polynomial with the sum and product of whose zeroes are -3 and 2 is x2 + 3x + 2. In a quadratic polynomial, the coefficients of the variables have a direct relationship to the sum and product of zeros. The sum and product of zeros can then be calculated with great ease, even when the zero values of a polynomial are unknown. The values of the variable for which the polynomial as a whole has 0 value are known as the polynomial’s zeros.

Table of content

1. Quadratic Polynomial whose Sum and Product of Zeroes are -3 and 2
2. Find a quadratic polynomial, the sum and product of whose zeroes are – 3 and 2 respectively.

Quadratic Polynomial whose Sum and Product of Zeroes are -3 and 2

The question states Find a quadratic polynomial, the sum and product of whose zeroes are – 3 and 2 respectively. Using fundamental algebraic principles and factorization ideas, any polynomial can be solved with ease. Setting the right-hand side as 0 is the first step in solving the polynomial equation. There are two distinct approaches to explaining a polynomial solution:

Solving Linear Polynomials
Solving Quadratic Polynomials

The steps to find a quadratic polynomial, the sum and the product whose zeros are -3 and 2 are as follows:

Let the zeroes be α and β

According to the given question we can write as α + β = -3 and αβ = 2

The quadratic polynomial whose product and the sum of zeroes are specified is defined as follows:

x2 – (α + β)x + αβ

Then the quadratic polynomial will be :

= x2 – (-3)x + 2

= x2 + 3x + 2

Summary: