Question

Find the zeros of the quadratic polynomial and verify the relation between zeros and coefficients of 4s^2 -4s+1

Answer 1

Step-by-step explanation:

The given polynomial is: 4s^2-4s+1

Factorising by splitting the middle term:

Sum= –4

Product= 4

4s^2–2s–2s+1

2s(2s–1)–1(2s–1)

(2s–1)(2s–1)=0

s=1/2 and s=1/2 (Both the zeroes are the same).

Sum of zeroes= 1/2 + 1/2 = 1

=–coefficient of s^2 / coefficient of s

Product of zeroes= 1/2 x 1/2 = 1/4

=constant term/coefficient of s^2

Answer 2

4s^2-2s-2s+1

2s(2s-1)-1(-2s+1)

(2s-1)(2s-1)

2s-1=0. 2s-1=0

2s=1. 2s=1

s=1/2. s=1/2

sum of zeroes=-b/a

=-(-4)/4

=1

=-coefficient of s/coefficient of x^2

product of zeroes=c/a

=1/4

=constant term/coefficient of x^2