Question

check wheather the quadratic equation ( x-2) (x + 1 )= (x -1 ) (x + 3 )​

Answer 1

    (x-2) (x+1) = (x-1) (x+3)

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

x² + x - 2x - 2 = x² - 3x - x + 3

       x² - x - 2 = x² - 4x + 3

-x + 4x - 2 - 3 = 0

            3x - 5 = 0

As the eqn. doesn't have degree as 2,

the given eqn. isn't quadratic.

Answer 2

Question: Check whether $(x-2)(x+1)=(x-1)(x+3)$ is a quadratic equation.

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

⇒ $x^{2} -x-2=x^{2} +2x-3$

⇒ $3x-1=0$

It is not of the form $ax^{2} +bx+c=0$

Hence, the given equation is not a quadratic equation.