# Choose the correct answer from the given four options in the following questions:Which of the following is not a quadratic equation?(A) $2(x-1)^{2}=4 x^{2}-2 x+1$(B) $2 x-x^{2}=x^{2}+5$(C) $(\sqrt{2} x+\sqrt{3})^{2}+x^{2}=3 x^{2}-5 x$(D) $\left(x^{2}+2 x\right)^{2}=x^{4}+3+4 x^{3}$

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To do:

We have to find the correct answer.

Solution:

$2(x-1)^{2} =4 x^{2}-2 x+1$

$2(x^{2}+1-2 x) =4 x^{2}-2 x+1$

$2 x^{2}+2-4 x =4 x^{2}-2 x+1$

$2 x^{2}+2 x-1 =0$ which represents a quadratic equation as it is in the quadratic equation form $a x^{2}+b x+c=0, a ≠0$

$2 x-x^{2} =x^{2}+5$

$2 x^{2}-2 x+5 =0$ which also represents a quadratic equation as it is in the quadratic equation form $a x^{2}+b x+c=0, a ≠ 0$.

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

$2 x^{2}+3+2 \sqrt{6}x =3 x^{2}-5 x$

$x^{2}-(5+2 \sqrt{6}) x-3 =0$ which also represents a quadratic equation as it is in the quadratic equation form $a x^{2}+b x+c=0, a ≠ 0$

$(x^{2}+2 x)^{2}=x^{4}+3+4 x^{2}$

$x^{4}+4 x^{2}+4 x^{3} =x^{4}+3+4 x^{2}$

$4 x^{3}-3=0$ which is not of the form $a x^{2}+b x+c, a ≠ 0$.

Therefore, the equation is not quadratic.

Updated on 10-Oct-2022 13:27:26