Which of the following is a quadratic equation?
The standard form of a quadratic equation is given by,
ax2 + bx + c = 0, a ≠ 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 – 
)
⇒ -2x2 = 10x - 2x2 – 2 + 
∴ 52x – 10 = 0
which is not a quadratic equation.
C. Given, (k + 1) x2 + 
= 7, where k = -1
⇒ (-1 + 1) x2 + 
= 7
∴ 3x – 14 = 0
which is not a quadratic equation.
D. Given, x3 - x2 = (x - 1)3
⇒ x3 - x2 = x3 - 3x2 + 3x - 1
∴ 2x2 - 3x + 1 = 0
which represents a quadratic equation.
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