Check whether the following are quadratic equations:
$x^3 -4x^2 -x + 1 = (x-2)^3$

AcademicMathematicsNCERTClass 10

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.   

raja
Updated on 10-Oct-2022 13:20:12

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