Question

Which of the following is not a quadratic equation?
(i) $(\sqrt{2}x+\sqrt{3}{)}^2=3x^2-5x$
(ii) $2x-x^2=x^2+5$
(iii) $(x^2+2x{)}^2=x^4+3+4x^2$

• A. (i) and (ii)
• B. (ii) and (iii)
• C. Only (iii)
• D. Only (ii)

Answer 1

The correct option is C

Only (iii)

(i) Given that, $(\sqrt{2}x+\sqrt{3}{)}^2=3x^2-5x$
$\Rightarrow 2x^2+3+2\sqrt{6}x=3x^2-5x\Rightarrow x^2-(5+2\sqrt{6})x-3=0$
which represents a quadratic equation because it is in the quadratic form $a{x}^2+bx+c=0,a\ne 0$

(ii) Given that, $2x-x^2=x^2+5$
$\Rightarrow 2x^2-2x+5=0$
which represents a quadratic equation because it is in the quadratic form $a{x}^2+bx+c=0,a\ne 0$

(iii) Given that, $(x^2+2x{)}^2=x^4+3+4x^2$
$\Rightarrow x^4+4x^2+4x^3=x^4+3+4x^2\Rightarrow 4x^3-3=0$
which is not of the form $a{x}^2+bx+c,a\ne 0$. Thus, the equation is not quadratic. This is a cubic equation.