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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.
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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 righthand 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:
Find a quadratic polynomial, the sum and product of whose zeroes are – 3 and 2 respectively.
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. Any polynomial may be solved with ease using basic algebraic concepts and factorization techniques. The first step in resolving the polynomial equation is to set the righthand side equal to 0.
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