Q1 of 44 Page 67

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

4s2 – 4s + 1

p(s) = 0

⇒ 4s2 – 4s + 1 = 0


⇒ 4s2 – 2s – 2s + 1 = 0


⇒ 2s(2s – 1) – 1(2s – 1) = 0


⇒ (2s – 1) (2s – 1) = 0


⇒ x = 1/2 and x = 1/2


Hence, 1/2 and 1/2 are zeroes of the polynomial 4s2 – 4s + 1.


Now,


Sum of zeroes = 1/2 + 1/2


⇒ Sum of zeroes = 1





Product of zeroes = 1/2 × 1/2


⇒ Product of zeroes = 1/4




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