Question

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

$t^2-15$

Answer 1

$t^2-15$

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

We get, a = 1, b = 0 and c = -15

We have, $t^2$ - 0.t - 15

$=(t-\sqrt{15})(t+\sqrt{15})$

The value of $t^2$ - 15 is zero when t - $\sqrt{15}$ = 0 or t + $\sqrt{15}$ = 0, i.e., when t = $\sqrt{15}$ or t = -$\sqrt{15}$

Therefore, the zeroes of $t^2$ - 15 are $\sqrt{15}$ and -$\sqrt{15}$
Sum of zeroes = $\sqrt{15}$ + -$\sqrt{15}=0=\frac{-0}{1}=\frac{-\left(Coefficientoft\right)}{Coefficientof{t}^2}$
Product of zeroes = $\left(\sqrt{15}\right)(-\sqrt{15})=-15=\frac{-15}{1}=\frac{Constantterm}{Coefficientof{t}^2}$