Question

STATEMENT - 1 : $(x-2)(x+1)$ $=$ $(x-1)(x+3)$ is a quadratic equation.
STATEMENT - 2 : If $p\left(x\right)$ is a quadratic polynomial, then $p\left(x\right)$ $=$ $0$ is called a quadratic equation.

• A. Statement - 1 is True, Statement - 2 is True, Statement - 2 is a correct explanation for Statement - 1
• B. Statement - 1 is True, Statement - 2 is True : Statement 2 is NOT a correct explanation for Statement - 1
• C. Statement - 1 is True, Statement - 2 is False
• D. Statement - 1 is False, Statement - 2 is True

Answer 1

The correct option is D Statement - 1 is False, Statement - 2 is True

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

To find whether the given equation is a quadratic equation or not

Sol:

$(x-2)(x+1)=(x-1)(x+3)⟹x^2+x-2x-2=x^2+3x-x-3⟹x^2-x^2+x-2x-3x+x-2+3=0⟹-3x+1=0$

This is not a quadratic equation as an equation of degree two is called a quadratic equation.

And, a polynomial when equated to zero or some value becomes an equation.