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Quadratic Equations

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Question

Check whether the following are Quadratic equations
$x^{2} + 3 x + 1 = {(x - 2)}^{2}$

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Solution

$x^{2} + 3 x + 1 = {(x - 2)}^{2}$
$x^{2} + 3 x + 1 = x^{2} - 4 x + 4$
$\Rightarrow x^{2} + 3 x + 1 - x^{2} + 4 x - 4 = 0$
$\Rightarrow 7 x - 3 = 0$ has its highest power of variable as $1$
Hence it is not a quadratic equation.

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