Question

Find the zeros of the following quadratic polynomials and verify the relationship between the zeros and the coefficients.
$3x^2-x-4$

Answer 1

${3x}^2-x-4=0$

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

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

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

$\therefore$ $x=-1$ or $4/3$

the roots are $-1$ and $4/3$

products of the roots $=-4/3$

Also, product of the roots $=\frac{constantterm}{coefficientof{x}^2}=\frac{-4}{3}$

Sum of the roots $=-1+\frac{4}{3}=+\frac{1}{3}$

Also, sum of the roots $=(-1)\frac{coefficientofx}{coefficientof{x}^2}=(-1)\frac{-1}{3}=\frac{1}{3}$