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Check whether the following are quadratic equations:
$x^3 -4x^2 -x + 1 = (x-2)^3$
Given:
Given equation is $x^3 -4x^2 -x + 1 = (x-2)^3$
To do:
We have to check whether the given equation is quadratic.
Solution:
The standard form of a quadratic equation is $ax^2+bx+c=0$.
$x^3 -4x^2 -x + 1 = (x-2)^3$
$x^3 - 4x^2 - x + 1 = x^3-2^3 + 3(x)(-2)(x - 2)$
$x^3 - 4x^2 -x + 1 = x^3 - 6x^2 + 12x - 8$
$x^3-x^3-4x^2+6x^2 - x-12x + 1+8 = 0$
$2x^2-13x+9=0$ is not of the form $ax^2+bx+c=0$
Therefore, $x^3 -4x^2 -x + 1 = (x-2)^3$ is not a quadratic equation.
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