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

4s^{2} – 4s + 1

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#### Solution

4s^{2} – 4s + 1 = 4s^{2} – 2s - 2s + 1

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

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

=`2(s - 1/2)2(s - 1/2)`

Therefore the zeroes of the polynomial are 1/2, 1/2

Relationship between the zeroes and the coefficient of the polynomial:

Also sum of the zeroes = `1/2+1/2 =1`

Also product of the zeroes = `1/2xx1/2=1/4`

hence verfied.

Concept: Relationship Between Zeroes and Coefficients of a Polynomial

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