Question 1(vii)

Check whether the following is a quadratic equation:
(vii) $(x + 2)^{3} = 2 x (x^{2} - 1)$

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Solution

(vii)
$(x + 2)^{3} = 2 x (x^{2} - 1) \Rightarrow x^{3} + 8 + 6 x^{2} + 12 x = 2 x^{3} - 2 x \Rightarrow x^{3} - 6 x^{2} - 14 x - 8 = 0$
It is not of the form $a x^{2} + b x + c = 0$
Hence, the given equation is not a quadratic equation.

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