Simplify $(x - 4) (2 x - 3) = 0$ and check whether it is a quadratic equation.

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Solution

We know that the general form of quadratic equation is $a x^{2} + b x + c = 0$ .

The given equation is $(x - 4) (2 x - 3) = 0$ can be simplified as follows:

$(x - 4) (2 x - 3) = 0 \Rightarrow x (2 x - 3) - 4 (2 x - 3) = 0 \Rightarrow 2 x^{2} - 3 x - 8 x + 12 = 0 \Rightarrow 2 x^{2} - 11 x + 12 = 0$

Since the equation $2 x^{2} - 11 x + 12 = 0$ is of the form $a x^{2} + b x + c = 0$ .

Hence, the equation $(x - 4) (2 x - 3) = 0$ is a quadratic equation.

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