Find the quadratic polynomial whose zeroes are 3 and -5.
By BYJU'S Exam Prep
Updated on: October 17th, 2023
The quadratic polynomial whose zeroes are 3 and -5 is x2 + 2x – 15. The coefficients of the variables in a quadratic polynomial are directly related to the sum and product of zeros. Then, even when the zero values of a polynomial are unknown, the sum and product of zeros can be determined relatively easily. The polynomial’s zeros are the values of the variable for which the polynomial as a whole has a value of 0.
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Quadratic Polynomial whose Zeroes are 3 and -5
The question states Find the quadratic polynomial whose zeroes are 3 and -5.” A polynomial may have some values of the variable for which it will have a zero value. These numbers are referred to as polynomial zero. They are also sometimes referred to as polynomial roots. To obtain the solutions to the given problem, we often determine the zeros of quadratic equations. There are two distinct approaches to explaining a polynomial answer:
- Solving Linear Polynomials
- Solving Quadratic Polynomials
The steps to find a quadratic polynomial whose zeroes are 3 and -5 are as follows:
Step 1: Let the zeroes be α and β
x2 – (sum of zeroes)x + (product of zeroes) = 0
x2 – (α + β)x + αβ
Step 2: Find the value of α + β and αβ
Since α = 3 and β = -5
Sum of zeroes = α + β = 3 + (-5) = -2
Product of zeroes = αβ = 3*(-5) = -15
Step 3: Substitute the values to form a quadratic polynomial
x2 – (α + β)x + αβ
x2 – (-2)x + (-15)
x2 + 2x – 15
Hence, the quadratic polynomial whose zeroes are 3 and -5 is x2 + 2x – 15.
Summary:
Find the quadratic polynomial whose zeroes are 3 and -5.
x2 + 2x – 15 is the quadratic polynomial with zeroes at 3 and -5. Division, subtraction, multiplication, and addition are polynomial operations. Any polynomial can be easily solved using fundamental algebraic ideas and factorization strategies. Setting the right-hand side of the polynomial equation equal to zero is the first step in solving it.
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