Question

Simplify $(2x-1)(x-3)=(x+5)(x-1)$ and check whether it is a quadratic equation.

Answer 1

We know that the general form of quadratic equation is $a{x}^2+bx+c=0$.

The given equation is $(2x-1)(x-3)=(x+5)(x-1)$ can be simplified as follows:

$(2x-1)(x-3)=(x+5)(x-1)\Rightarrow 2x(x-3)-1(x-3)=x(x-1)+5(x-1)\Rightarrow 2x^2-6x-x+3=x^2-x+5x-5\Rightarrow 2x^2-7x+3=x^2+4x-5\Rightarrow 2x^2-7x+3-x^2-4x+5=0\Rightarrow x^2-11x+8=0$

Since the equation $x^2-11x+8=0$ is of the form $a{x}^2+bx+c=0$.

Hence, the equation $(2x-1)(x-3)=(x+5)(x-1)$ is a quadratic equation.