Find the zeroes of the following polynomial 5×2-4-8x and verify the relationship between zeros of the polynomial and the coefficients of the polynomial.
By BYJU'S Exam Prep
Updated on: October 17th, 2023
The zeroes of the polynomial 5×2-4-8x are 2, -⅖. The word “polynomial” is made up of the words “nominal,” which means “terms,” and “poly,” which means “many.” A polynomial (No division operation by a variable) is an expression made up of variables, constants, and exponents that are combined using mathematical operations including addition, subtraction, multiplication, and division.
Depending on how many terms are included, the expression is classified as a monomial, binomial, or trinomial. In this post, we will go through the step-by-step solution for the question “Find the zeroes of the following polynomial 5×2-4-8x and verify the relationship between zeros of the polynomial and the coefficients of the polynomial.”
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5×2 – 4 – 8x, Find the Zeros.
The question states Find the zeroes of the following polynomial 5×2-4-8x and verify the relationship between zeros of the polynomial and the coefficients of the polynomial.” The zeros of the following quadratic polynomials 5×2 – 4 – 8x are 2, -⅖, and the relationship between the zeroes and the coefficients of the polynomial is verified in the below steps. Follow these three steps to find the zeros of the following quadratic polynomials 5×2-4-8x:
Step 1: Factorise the polynomial and find its zeroes.
5×2 – 8x – 4 = 5×2 – 10x + 2x – 4
5x (x – 2) + 2(x – 2)
(x – 2) (5x + 2)
x = 2, -⅖
Step 2: Verify the relationship between zeros and coefficients of the polynomial.
The sum of zeros = 2 + (-⅖)
2 – ⅖
(10 – 2)/5
8/5 = -b/a
The product of zeros = 2 * (-⅖)
-⅘ = c/a
Hence, the zeroes of the polynomial 5×2 – 4 – 8x are 2, -⅖.
Summary:
Find the zeroes of the following polynomial 5×2-4-8x and verify the relationship between zeros of the polynomial and the coefficients of the polynomial.
The zeros of the quadratic polynomial 5×2-4-8x are 2, -⅖, and the relationship between the zeroes and the coefficients of the polynomial is verified. By substituting values in the sum of the zeroes = -b/a and the product of the roots = c/a, we can easily find the zeros of the quadratic polynomial 5×2 – 4 – 8x.
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