Question

Which of the following is a quadratic equation? 

(a)${\displaystyle (x^2+1)={(2-x)}^2+3}$              (b)${\displaystyle x^3-x^2={(x-1)}^3}$ 

(c) ${\displaystyle 2x^{+}3=(5+x)(2x-3)}$                (d) None of these  

Answer 1

${\displaystyle x^3-x^2={(x-1)}^3}$ 

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

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

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