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Quadratic Equation

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Question

Check whether the following are Quadratic equations
$(2 x - 1) (x - 3) = (x + 5) (x - 1)$

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Solution

$(2 x - 1) (x - 3) = (x + 5) (x - 1)$
$\Rightarrow 2 x^{2} - 6 x - x + 3 = x^{2} - x + 5 x - 5$
$\Rightarrow 2 x^{2} - 6 x - x + 3 = x^{2} + 4 x - 5$
$\Rightarrow 2 x^{2} - 7 x + 3 - x^{2} - 4 x + 5 = 0$
$\Rightarrow x^{2} - 8 x + 8 = 0$
The above equation is a quadratic one as the degree (highest power of the variable) of the equation is $2.$

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(2 x - 1) (x - 3) = (x + 5) (x - 1)

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and check whether it is a quadratic equation.

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