Mathematics
Check whether the following is quadratic equation :
x3 - 4x2 - x + 1 = (x - 2)3
Quadratic Equations
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Answer
Given,
Equation : x3 - 4x2 - x + 1 = (x - 2)3
⇒ x3 - 4x2 - x + 1 = x3 - 23 - 3.x.2(x - 2)
⇒ x3 - 4x2 - x + 1 = x3 - 8 - 6x(x - 2)
⇒ x3 - x3 - 4x2 - x + 1 + 8 = -6x2 + 12x
⇒ -4x2 + 6x2 - x - 12x + 9 = 0
⇒ 2x2 - 13x + 9 = 0.
The above equation is of the form ax2 + bx + c = 0.
Hence, the above equation is a quadratic equation.
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