Question

Question 1 (i)
Find the zeroes of the following quadratic polynomials and verify the relationship between the zeroes and the coefficients.
$x^2-2x-8$

Answer 1

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

We get, a = 1, b = - 2 and c = -8

We have, $x^2–2x-8$ = $x^2–4x+2x–8$

= x (x-4) +2 (x-4)

= (x+2) (x-4)

Equating this to 0, we will get the values of 2 zeroes of the polynomial.

(x-4)(x+2) = 0

$\Rightarrow$ x = -2 and 4 are two zeroes.

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

Product of zeroes = 4 $\times$ (-2) = -8 = $\frac{-8}{1}=\frac{Constantterm}{Coefficientof{x}^2}$.
(Relationship between the zeroes and the coefficients)