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Find the zeros of the following quadratic polynomials 4s2 – 4s + 1 and verify the relationship between the zeros and the coefficients.
By BYJU'S Exam Prep
Updated on: September 25th, 2023
The zeros of the quadratic polynomial 4s24s+1 are ½, ½. 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.
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4s24s+1 Find the Zeros
The question states Find the zeros of the following quadratic polynomials 4s ^ 2 – 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 in the below steps. Follow these three steps to find the zeros of the following quadratic polynomials 4s24s+1:
Step 1: Form the equation
The given polynomial is 4s24s+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 4s24s+1 is verified. Hence, the zeroes of this polynomial are ½ and ½.
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 quadratic polynomial 4s2 – 4s + 1 are ½, ½ 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 4s24s+1.
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