Question

Check whether the following is quadratic equation.
$(2x-1)(x-3)=(x+5)(x-1)$

Answer 1

Sol :- Given

$(2x-1)(x-3)=(x+5)(x-1)$

also given, to check whether the given Equation is

in a quadratic form

So, let us now Expand the given Equation we get,

$(2x-1)(x-3)=(x+5)(x-1)$

$\Rightarrow 2x^2-6x-x+3=x^2-x+5x-5$

by further simplification we get,

$\Rightarrow 2x^2-7x+3=x^2+4x-5$

$\Rightarrow 2x^2-x^2-7x-4x+3+5=0$

$\Rightarrow x^2-11x+8=0\to eq\left(1\right)$

Here eq (1) represent a quadratic from of

$a{x}^2+bx+c=0$

where, $a=1,b=-11,c=8$

So the given $(2x-1)(x-3)=(x+5)(x-1)$ is a

quadratic Equation.