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

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Solution

Quadratic equation:
Quadratic equations are the polynomial equations of degree $2$ in one variable of type ${ax}^{2} + bx + c$ where $a, b, c, \in R$ and $a \neq 0$ .
On expanding the given equation $(x - 2) (x + 1) = (x - 1) (x + 3)$ , we get
$\begin{array}{rcl} (x - 2) (x + 1) & = & (x - 1) (x + 3) \\ x^{2} + 1 x - 2 x - 2 & = & x^{2} + 3 x - 1 x - 3 \\ x^{2} - 1 x - 2 & = & x^{2} + 2 x - 3 \\ x^{2} - x^{2} - 1 x - 2 x - 2 + 3 & = & 0 \\ - 3 x + 1 & = & 0 \end{array}$
$∵$ The above equation is not in the form of ${ax}^{2} + bx + c = 0$
Therefore, the given equation $(x - 2) (x + 1) = (x - 1) (x + 3)$ is not a quadratic equation.

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Question 1(i)
Check whether the following are quadratic equations:
$(i) (x + 1)^{2} = 2 (x - 3)$

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