Question

Question 1 (ii)
Find the zeroes of the following quadratic polynomials and verify the relationship between the zeroes and the coefficients.

$4s^2-4s+1$

Answer 1

$4s^2-4s+1$

Comparing given polynomial with the general form $a{x}^2+bx+c$,

We get, a = 4, b = -4 and c = 1.

We have, $4s^2-4s+1$ = $(2s-1{)}^2$

The value of $4s^2-4s+1$ is zero when $(2s-1{)}^2$ = 0.
$\Rightarrow$ s = $\frac{1}{2}$

Therefore, the zeroes of $4s^2-4s+1$ are $\frac{1}{2}and\frac{1}{2}$.

Sum of zeroes
= $\frac{1}{2}+\frac{1}{2}=1=-\frac{(-4)}{4}=\frac{-\left(Coefficientofs\right)}{Coefficientof{s}^2}$

Product of zeroes
=$\frac{1}{2}\times \frac{1}{2}=\frac{1}{4}=\frac{Constantterm}{Coefficientof{s}^2}$
(Relationship between the zeroes and the coefficients)