Which of the following is a quadratic equation?

Question

KollegeApply · Accepted Answer

x3 – x2 = (x – 1)3 Explanation: The standard form of a quadratic equation is given by, ax2 + bx + c = 0, a $\neq$ 0 (A) Given, x2 + 2x + 1 = (4 – x)2 + 3 x2 + 2x + 1 = 16 – 8x + x2 + 3 10x – 18 = 0 which is not a quadratic equation. (B) Given, –2x2 = (5 - x)(2x - $\frac{2}{5}$) –2x2 = 10x - 2x^2 - 2 + (2x)/5 50x + 2x – 10 = 0 52x – 10 = 0 which is not a quadratic equation. (C) Given, (k + 1)x^2 + $\frac{3}{2}$x = 7, where k = –1 (-1 + 1)x^2 + $\frac{3}{2}$x = 7 3x – 14 = 0 which is not a quadratic equation. (D) Given, x3 – x2 = (x – 1)3 x3 – x2 = x3 – 3x2(1) + 3x(1)2 – (1)3 ...[ ∵ (a – b)3 = a3 – b3 + 3ab2 – 3a2b] x3 – x2 = x3 – 3x2 + 3x – 1 –x2 + 3x2 – 3x + 1 = 0 2x2 – 3x + 1 = 0 which represents a quadratic equation.

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