Question

Find the zeros of the quadratic polynomial 4x² − 4x − 3 and verify the relation between the zeros and the coefficients.

Answer 1

We have

$f\left(x\right)=4x^2-4x-3$

$f\left(x\right)=4x^2-(6x-2x)-3$

$f\left(x\right)=4x^2-6x+2x-3$

$f\left(x\right)=2x(2x-3)+1(2x-3)$

$f\left(x\right)=(2x+1)(2x-3)$

∴f(x)=0

=>(2x+1)(2x−3)=0

=>2x+1=0 or 2x−3=0

=>x=−1/2 or x=3/2

So, the zeros of f(x) are −1/2 and 3/2.

$Sumofthezeros=-1/2+3/2=(-1+3)/2=22=1=-\left(coefficientofx\right)/\left(coefficientof{x}^2\right)$

$Productofthezeros=-12\times 32=-34=constantterm/\left(coefficientof{x}^2\right)$