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

Given:

Given equation is $x^2 + 3x + 1 = (x – 2)^2$

To do:

We have to check whether the given equation is quadratic.

Solution:

The standard form of a quadratic equation is $ax^2+bx+c=0$.

$x^2 + 3x + 1 = (x – 2)^2$

$x^2 + 3x + 1 = x^2 – 2(x)(2)+(2)^2$

$x^2 + 3x + 1 = x^2-4x+4$

$x^2-x^2+3x+4x+1-4=0$

$7x-3=0$ is not of the form $ax^2+bx+c=0$

Therefore, $x^2 + 3x + 1 = (x – 2)^2$ is not a quadratic equation.  

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Updated on: 10-Oct-2022

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