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Quadratic Equations
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29/05/2021 12:20 pm
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Check whether the following are quadratic equations:
(i) (x + 2)3 = 2x (x2 – 1)
(ii) x3 – 4x2 – x + 1 = (x – 2)3
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29/05/2021 12:21 pm
(i) Given, (x + 2)3 = 2x(x2 – 1)
By using the formula for (a + b)2 = a2+ 2ab+b2
⇒ x3 + 8 + x2 + 12x = 2x3 – 2x
⇒ x3 + 14x – 6x2 – 8 = 0
Since the above equation is not in the form of ax2 + bx + c = 0.
Therefore, the given equation is not a quadratic equation.
(ii) Given, x3 – 4x2 – x + 1 = (x – 2)3
By using the formula for (a + b)2 = a2+ 2ab+b2
⇒ x3 – 4x2 – x + 1 = x3 – 8 – 6x2 + 12x
⇒ 2x2 – 13x + 9 = 0
Since the above equation is in the form of ax2 + bx + c = 0.
Therefore, the given equation is quadratic equation.