Question

Find the zeros of the following quadratic polynomials and verify the relationship between the zeros and the coefficients.
$t^2-15$

Answer 1

Let $f\left(t\right)=t^2-15$

To calculate the zeros of the given equation, put $f\left(t\right)=0$.

$t^2-15=0$

$\left(t+\sqrt{15}\right)\left(t-\sqrt{15}\right)=0$

$t=\sqrt{15},t=-\sqrt{15}$

The zeros of the given equation is $\sqrt{15}$ and $-\sqrt{15}$.

Sum of the zeros is $\sqrt{15}+\left(-\sqrt{15}\right)=0$.

Product of the zeros is $\sqrt{15}\times -\sqrt{15}=-15$.

According to the given equation,

The sum of the zeros is,

$\frac{-b}{a}=\frac{-\left(0\right)}{1}$

$=0$

The product of the zeros is,

$\frac{c}{a}=\frac{-15}{1}$

$=-15$

Hence, it is verified that,

$sumofzeros=\frac{-coefficientofx}{coefficientof{x}^2}$

And,

$productofzeros=\frac{constantterm}{coefficientof{x}^2}$