Find a quadratic polynomial, the sum, and product of whose zeros are -3 and 2.

By Ritesh|Updated : November 9th, 2022

The quadratic polynomial with the sum and product of whose zeros are -3 and 2 is x2 + 3x + 2. Steps to find a quadratic polynomial, the sum, and the product of whose zeros are -3 and 2:

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

Quadratic Polynomial

Polynomial is formed composed of the phrases Nominal, which means "terms," and Poly, which means "many." An expression that consists of variables, constants, and exponents that is combined using mathematical operations like addition, subtraction, multiplication, and division is referred to as a polynomial (No division operation by a variable). The expression is divided into three categories: monomial, binomial, and trinomial depending on how many terms are included in it.

Using fundamental algebraic principles and factorization ideas, any polynomial may 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

There are four main polynomial operations which are:

  • Addition of Polynomials
  • Multiplication of Polynomials
  • Subtraction of Polynomials
  • Division of Polynomials

Summary:

Find a quadratic polynomial, the sum, and the product of whose zeros are -3 and 2.

The quadratic polynomial with the sum and product of whose zeros are -3 and 2 is x2 + 3x + 2. The polynomial operations are division, subtraction, multiplication, and addition.

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