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Quadratic Equations
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29/05/2021 12:18 pm
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Check whether the following are quadratic equations:
(i) (2x – 1)(x – 3) = (x + 5)(x – 1)
(ii) x2 + 3x + 1 = (x – 2)2
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29/05/2021 12:19 pm
(i) Given, (2x – 1)(x – 3) = (x + 5)(x – 1)
By using the formula for (a + b)2 = a2+2ab+b2
⇒ 2x2 – 7x + 3 = x2 + 4x – 5
⇒ x2 – 11x + 8 = 0
Since the above equation is in the form of ax2 + bx + c = 0.
Therefore, the given equation is quadratic equation.
(ii) Given, x2 + 3x + 1 = (x – 2)2
By using the formula for (a + b)2=a2+2ab+b2
⇒ x2 + 3x + 1 = x2 + 4 – 4x
⇒ 7x – 3 = 0
Since the above equation is not in the form of ax2 + bx + c = 0.
Therefore, the given equation is not a quadratic equation.