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
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