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Question
Choose the correct answer from the given four options :
Which of the following is not a quadratic equation?
Options
(x + 2)2 = 2(x + 3)
x2 + 3x = ( – 1) (1 – 3x)
(x + 2) (x – 1) = x2 – 2x – 3
x3 – x2 + 2x + 1 = (x + 1)3
Solution
(x + 2)2 = 2(x + 3)
⇒ x2 + 4x + 4 = 2x + 6
⇒ x2 + 4x – 2x + 4 – 6 = 0
⇒ x2 + 2x – 2
It is a quadratic equation.
x2 + 3x = ( – 1) (1 – 3x)
⇒ x2 + 3x = –1 + 3x
⇒ x2 + 1 = 0
it is also quadratic equation.
(x + 2) (x – 1) = x2 – 2x – 3
x2 - x + 2x - 2 = x2 - 2x - 3
x2 - x2 + x + 2x - 2 + 3 = 0
⇒ 3x + 1 = 0
It is not a quadratic equation.
x3 – x2 + 2x + 1 = (x + 1)3
= x3 + 3x2 + 3x + 1
x3 - x2 + 2x + 1
3x2 + x2 - 2x - 1 + 3x + 1 = 0
⇒ 4x2 + x = 0
It is a quadratic equation.
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