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

$h(t)\ =\ t^2\ –\ 15$

Given:


$h(t) = t^2 – 15$

To find:

Here, we have to find the zeros of h(t). 

Solution:

To find the zeros of h(t), we have to put $h(t)=0$.

This implies,

$t^2 – 15 = 0$

$t^2 – \sqrt{(15)^2} = 0$

$(t+\sqrt{15})(t-\sqrt{15})= 0$  (since $a^2-b^2=(a+b) (a-b) $) 

$t+\sqrt{15}=0$ and $t-\sqrt{15}=0$

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

Therefore, the zeros of the quadratic equation $h(t) = t^2 – 15 $ are $-\sqrt{15}$ and $\sqrt{15}$.

Verification:

We know that, 

Sum of zeros $= -\frac{coefficient of t}{coefficient of t^2}$

                       $= –\frac{0}{1}$  (Coefficient of t is 0) 

                       $=0$

Sum of the zeros of $h(t)=-\sqrt{15}+\sqrt{15}=0$

Product of roots $= \frac{constant}{coefficient of t^2}$

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

                           $=-15$

Product of the roots of $h(t)=-\sqrt{15}\times\sqrt{15}=-15$

Hence, the relationship between the zeros and their coefficients is verified.

Updated on: 10-Oct-2022

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