Question

Find the zeroes of quadratic equation 4s² - 4s + 1. Also find the relationship between the zeroes and the coefficient.

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Answer 1

Answer:

4s2-4s+1=0

4s2-2s-2s+1=0

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

s=1/2 , s=1/2

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Answer 2

Given

Find the zeroes of quadratic equation 4s² - 4s + 1. Also find the relationship between the zeroes and the coefficient.

Answer

quadratic polynomial = 4s²- 4s +1= q(y)

to find the zeroes of the given quadratic polynomial,

q(y) = 0

4s² - 4s+1 = 0

⇒4s²-2s-2s+1 = 0

⇒2s(2s-1)-1(2s-1) = 0

⇒(2s-1) (2s-1) = 0

⇒2s - 1  = 0 ; 2s - 1= 0

⇒s = 1/2, 1/2

therefore, the zeroes of the polynomial = 1/2,1/2

now,

sum of the zeroes = 1/2 + 1/2 = 2/2 = -(co-efficient of s)

                                                             (co-efficient of s²)

product of the zeroes = 1/2(1/2) = 1/4 = constant term / coefficient of s²

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