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## Question 1. Find the zeroes of the following quadratic polynomials and verify the relationship between the zeroes and the coefficients. (ii) 4s² – 4s + 1

1. Find the zeroes of the following quadratic polynomials and verify the relationship between the zeroes and the coefficients.

(ii) 4s² – 4s + 1

Factorize the equation
Compare the equation with as²  + bs  + c  = 0
We get
a = 4 , b = -4, c = 1
To factorize the value we have to find two value which
sum is equal to            b           = -4
product is                   a x c      = 4
-2 and -2 are such number which
sum is (–  2)+(  – 2)                =  - 4
product is       (- 2 )* (- 2)       =    4
So we can write middle term             - 4s   = -2s – 2s
We get
4s² - 2s - 2s + 1 = 0

2s(2s -1) -1(2s -1) = 0
(2s - 1) (2s - 1) = 0

Solve for first zero

2s - 1     =0
2s         = 1
s           = ½

Solve for second zero

2s - 1     =0
2s         = 1
S          = ½

sum of zeros               ½ + ½       = 2/2    =  1
product of zeros          ½ x ½       = 1/4

Sum of zero = -b/a = -(-4/4) = 1

Product of zero= c/a =  1/4 = 1/4

Question 1. Find the zeroes of the following quadratic polynomials and verify the relation