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Question
Find the zeroes of the following quadratic polynomial and verify the relationship between the zeroes and the coefficients:
4s2 – 4s + 1
Solution
4s2 – 4s + 1
= 4s2 – 2s - 2s + 1
= 2s(2s - 1) - 1(2s - 1)
= (2s - 1)(2s -1)
For p(s) = 0, we have, (2s - 1) = 0
`s = 1/2`
∴ The zeroes of `4s^2 - 4s + 1 "are" 1/2 "and" 1/2`
= Sum of the zeroes `="-Coefficient of x"/"Coefficient of x"`
= `1/2 + 1/2`
= `(-(-4))/4`
1 = 1
Product of the zeroes `="Constant term"/("Coefficient of "s^2)`
`(1/2)xx(1/2)= 1/4`
⇒ `1/4 = 1/4`
Thus, the relationship between the zeroes and coefficients in the polynomial 4s2 - 4s + 1 is verified.
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