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Question
Choose the correct answer from the given four options :
Which of the following is a quadratic equation?
Options
(x – 2) (x + 1) = (x – 1) (x – 3)
(x + 2)3 = 2x(x2 – 1)
x2 + 3x + 1 = (x – 2)2
8(x – 2)3 = (2x – 1)3 + 3
Solution
(x – 2) (x + 1) = (x – 1) (x – 3)
⇒ x2 + x – 2x – 2 = x2 – 3x – x + 3
⇒ 3x + x – 2x + x = 3 + 2
⇒ 3x = 5
It is not a quadratic equation
(x + 2)3 = 2x(x2 - 1)
x3 + 6x2 + 12x + 8 = 2x3 – 2x
x3 + 6x2 + 12x + 8 – 2x3 + 2x = 0
–x3 + 6x2 + 14x + 8 = 0
It is not a quadratic equation.
x2 + 3x + 1 = (x – 2)2
x2 + 3x + 1 = x2 – 4x + 4
3x + 1 + 4x – 4 = 0
⇒ 7x – 3 = 0
It is not a quadratic equation.
8(x – 2)3 = (2x – 1)3 + 3
8(x3 – 6x2 + 12x - 8) = 8x3 – 12x2 + 6x – 1+ 3
8x3 – 48x2 + 96x – 64 – 8x3 + 12x2 – 6x + 1 – 3 = 0
–36x2 + 90x – 66 = 0
It is a quadratic equation.
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