Question 1(viii)
Check whether the following are quadratic equations:
(viii) $x^{3} - 4 x^{2} - x + 1 = (x - 2)^{3}$

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Solution

(viii) $x^{3} - 4 x^{2} - x + 1 = (x - 2)^{3} \Rightarrow x^{3} - 4 x^{2} - x + 1 = x^{3} - 8 - 6 x^{2} + 12 x \Rightarrow 2 x^{2} - 13 x + 9 = 0$
It is of the form $a x^{2} + b x + c = 0$
Hence, the given equation is quadratic equation.

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