Which of the following is not a quadratic equation?

Question:

Which of the following is not a quadratic equation?

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

(b) $(x+2)^{2}=2\left(x^{2}-5\right)$

(c) $(\sqrt{2} x+3)^{2}=2 x^{2}+6$

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

 

Solution:

(c) $(\sqrt{2} x+3)^{2}=2 x^{2}+6$

$\because(\sqrt{2} x+3)^{2}=2 x^{2}+6$

$\Rightarrow 2 x^{2}+9+6 \sqrt{2} x=2 x^{2}+6$

$\Rightarrow 6 \sqrt{2} x+3=0$, which is not a quadratic equation

 

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