Question

Find the zeroes of the quadratic polynomial polynomial $5t^2+12t+7$ and verify the relationship between zeroes and the coefficients.

Answer 1

$5t^2+12t+7=0$

$5t^2+5t+7t+7=0$

$5t(t+1)+7(t+1)=0$

$(5t+7)(t+1)=0$

$\Rightarrow t=\frac{-7}{5}$ and $t=-1$

$\therefore$ sum of roots is $\frac{-7}{5}-1=\frac{-12}{5}$

$=\frac{-b}{a}$

product of roots = $\left(\frac{-7}{5}\right)(-1)=\frac{7}{5}$

$=\frac{c}{a}$

Hence verified