Question

Find the sum of the zeroes and the product of the zeroes of the quadratic polynomial $p\left(x\right)=3x^2+7x+4$, without finding the zeroes.

Answer 1

For $p\left(x\right)=3x^2+7x+4$, let $\alpha$ and $\beta$ be the zeroes of $p\left(x\right)$
Here $a=3,b=7,c=4$ .......... [By comparing with standard quadratic polynomial]
Sum of zeroes$=\alpha +\beta =-\frac{b}{a}=-\frac{Coefficientofx}{Coefficientof{x}^2}=-\frac{7}{3}$
Product of zeroes $=\alpha .\beta =\frac{c}{a}=\frac{Constantterm}{Coefficientof{x}^2}=\frac{4}{3}$