Question

Find the zeroes of the following quadratic polynomial and verify the relationship between the zeroes and the coefficients:

4s² – 4s + 1

Answer 1

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.