Question

Find the zeros and verify the relationship between zeroes and coefficients t ^2 -15

Answer 1

Answer:

Let $f(t)=t^2-15$

$f(t)=t^2-{\sqrt{15}}^2$

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

$\implies\bold{t=\sqrt{15},-\sqrt{15}}$ are zeros

$f(t)=t^2+0.t-15$

Sum of zeros$=\frac{0}{1}=0$

Product of zeros$=\frac{-15}{1}=-15$

$\bold{Verification:}$

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

Product of zeros$=(\sqrt{15})(-\sqrt{15})=-15$

Hence verified.

Answer 2

Answer:

Step-by-step explanation:

Let f(t)=t^2-15

f(t)=t^2-√15^2

f(t)=(t-√15)(t+√15)

t=√15,-√15 are zeros

f(t)=t^2+0.t-15

Sum of zeros=0/1=0

Product of zeros=-√15×√15=-15

Verification:

Sum of zeros=√15+(-√15)=0

Product of zeros=√15})(-√15)=-15

Hence verified.