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Question
Check whether the following is the quadratic equation:
x3 - 4x2 - x + 1 = (x - 2)3
Solution
x3 - 4x2 - x + 1 = (x - 2)3
⇒ x3 - 4x2 - x + 1 = x3 + 3x2(-2) + 3x(-2)2 + (-2)3
⇒ x3 - 4x2 - x + 1 = x3 - 6x2 + 12x - 8
⇒ x3 - 4x2 - x + 1 - x3 + 6x2 - 12x + 8 = 0
⇒ 2x2 - 13x + 9 = 0
It is of the form ax2 + bx + c = 0.
Hence, the given equation is a quadratic equation.
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