Check whether the following is quadratic equation.
$x^{3} - 4 x^{2} - x + 1 = (x - 2)^{3}$

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Solution

$x^{3} - 4 x^{2} - x + 1 = (x - 2)^{3} . . . (A)$
for a equation to be quadratic it is
similar to
$a x^{2} + b x + c = 0 . . . (1)$
where $a, b, c$ are integers
Now, from eq. (A)
$x^{3} - 4 x^{2} - x + 1 = (x - 2)^{3}$
$x^{3} - 4 x^{2} - x + 1 = x^{3} - 8 - 6 x + 12 x^{2}$
$16 x^{2} - 5 x - 9 = 0 . . . (2)$
On comparing eq (2) & (1)
we observe that eq (1) & (2) are
similar
Hence eq $(A)$ represent t a quadratic equation.

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Similar questions

x^{3} - {4 x}^{2} - x + 1 = {(x - 2)}^{3}

x^{3} - 4 x^{2} - x + 1 = (x - 2)^{3}

(x + 2)^{3} = 2 x (x^{2} - 1)

I s

x^{3} - 4 x^{2} - x + 1 = (x - 2)^{3}

{(x + 2)}^{3} = 2 x (x^{2} - 1)

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