Question

Find the zeros of the following quadratic polynomials and verify the relationship between the zeros and the coeffients :

$4x^2-4x-3$

Answer 1

The given quadratic polynomial is

$4x^2-4x-3=4x^2-6x+2x-3$

$=2x(2x-3)+1(2x-3)$

$=(2x+1)(2x-3)$

So the zeroes of the quadratic polynomial are

$-\frac{1}{2}and\frac{3}{2}$

Sum of zeros $\frac{-b}{a}=\frac{-(-4)}{4}=1$

Sum of zeroes $=-\frac{1}{2}+\frac{3}{2}=\frac{-1+3}{2}=\frac{2}{2}=1$

Product of zeros $\frac{c}{a}=\frac{-3}{4}$

Product of zeros $-\frac{1}{2}\times \frac{3}{2}=\frac{-3}{4}$

Hence proved that,

Sum of zeros $\frac{-\left(Coefficientofx\right)}{Coefficientof{x}^2}$

Product of zeros $\frac{Constantterm}{Coefficientof{x}^2}$