Which of the following is a quadratic equation?
Question:

Which of the following is a quadratic equation?

(a) $\left(x^{2}+1\right)=(2-x)^{2}+3$

(b) $x^{3}-x^{2}=(x-1)^{3}$

(c) $2 x^{2}+3=(5+x)(2 x-3)$

(d) None of these

Solution:

(b) $x^{3}-x^{2}=(x-1)^{3}$

$\because x^{3}-x^{2}=(x-1)^{3}$

$\Rightarrow x^{3}-x^{2}=x^{3}-3 x^{2}+3 x-1$

$\Rightarrow 2 x^{2}-3 x+1=0$, which is a quadratic equation