Question

Find the zeroes of the following quadratic polynomial and verify the relationship between the zeroes and the coefficients
$3x^2-x-4$

Answer 1

$3x^2-x-4=0$ (here a=3, b=-1, c=-4)

$\Rightarrow 3x^2-4x+3x-4=0$

$\Rightarrow 3x(x+1)-4(x+1)=0$

$\Rightarrow x=\frac{4}{3},-1$

Sum of roots$=\frac{4}{3}-1=\frac{1}{3}=\frac{-b}{a}$

Product of roots $=\frac{4}{3}(-1)=\frac{-4}{3}=\frac{c}{a}$