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# Choose the correct answer from the given four options in the following questions:

Which of the following is a quadratic equation?

**(A)** $ x^{2}+2 x+1=(4-x)^{2}+3 $

**(B)** $ -2 x^{2}=(5-x)\left(2 x-\frac{2}{5}\right) $

**(C)** $ (k+1) x^{2}+\frac{3}{2} x=7 $, where $ k=-1 $

**(D)** $ x^{3}-x^{2}=(x-1)^{3} $

**To do:**

We have to find the correct answer.

**Solution:**

$x^{2}+2 x+1=(4-x)^{2}+3$

$x^{2}+2 x+1=16+x^{2}-8x+3$

$10x-18=0$ which is not of the form $a x^{2}+b x+c, a≠0$.

Therefore, the equation $x^{2}+2 x+1=(4-x)^{2}+3$ is not a quadratic equation.

$-2 x^{2} =(5-x)(2 x-\frac{2}{5})$

$-2 x^{2}=10 x-2 x^{2}-2+\frac{2 x}{5}$

$50 x+2 x-10=0$

$52 x-10=0$ which is also not a quadratic equation.

$x^{2}(k+1)+\frac{3}{2} x=7$

$k=-1$

$x^{2}(-1+1)+\frac{3}{2} x=7$

$3 x-14=0$ which is also not a quadratic equation.

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

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

$x^{3}-x^{2} =x^{3}-3 x^{2}+3 x-1$

$-x^{2}+3 x^{2}-3 x+1 =0$

$2 x^{2}-3 x+1=0$ which represents a quadratic equation (it is of the quadratic form $a x^{2}+b x+c=0, a≠0$)

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