Question

Question 1 (iii)
Find the zeroes of the following polynomials by factorization method and verify the relations between the zeroes and the coefficient of the polynomials
(iii) $5t^2+12t+7$

Answer 1

iii) Let $f\left(t\right)=5t^2+12t+7$
$=5t^2+7t+5t+7$
$=t(5t+7)+1(5t+7)$
$=(5t+7)(t+1)$
So, the value of $5t^2+12t+7$ is zero when 5t + 7 = 0 or t + 1 = 0
i.e., when $t=\frac{-7}{5}ort=-1$
So, the zeroes of $5t^2+12t+7are-\frac{7}{5}and-1$
$\therefore$ Sum of zeroes $=-\frac{7}{5}-1=\frac{-12}{5}$
$=(-1)\left(\frac{Constantterm}{Coefficientof{t}^2}\right)$
and product of zeroes $(-\frac{7}{5})(-1)=\frac{7}{5}$
$=(-1{)}^2\left(\frac{Constantterm}{Coefficientof{t}^2}\right)$
Hence, verified the relations between the zeroes and the coefficients of the polynomial