Find the zeros of the following quadratic polynomials 4s2 - 4s + 1 and verify the relationship between the zeros and the coefficients.

By Ritesh|Updated : November 10th, 2022

The zeros of the following quadratic polynomials 4s2 - 4s + 1 are ½, ½, and the relationship between the zeroes and the coefficients of the polynomial is verified. Steps to find the zeros of the following quadratic polynomials 4s2 - 4s + 1:

Step 1: Form the equation

The given polynomial is 4s2 - 4s + 1

We are aware that a polynomial's zeroes are evaluated by equating them to zero.

p(s) = 0

Hence the above equation becomes 4s2 - 4s + 1 = 0.

Step 2: Solve to find the zeroes

4s2 - 4s + 1 = 0

The above equation can be written as:

(2s)2 - 2 (2s) + 12 = 0

(2s + 1)2 = 0 [As (a - b)2 = a2 - 2ab + b2]

s = ½, ½

Step 3: Verification

We know that for a given polynomial as2 + bs + c

Sum of the zeroes = -b/a and

product of the roots = c/a

Substituting the values in the above formula we get:

Sum of the zeroes = ½ + ½ = 1

Again, -b/a = - (-4)/4 = 1

Product of the zeroes = ½ x ½ = ¼

Again, c/a = ¼

Thus, the relationship between the zeroes and the coefficients of the polynomial is verified.

Hence, the zeroes of this polynomial are ½ and ½.

Quadratic Polynomials

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 are 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.

Summary:

Find the zeros of the following quadratic polynomials 4s2 - 4s + 1 and verify the relationship between the zeros and the coefficients.

The zeros of the following quadratic polynomials 4s2 - 4s + 1 are ½, ½ and the relationship between the zeroes and the coefficients of the polynomial is verified.

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