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Which of the following are quadratic equations?
$x\ –\ \frac{3}{x}\ =\ x^2$
Given:
Given quadratic equation is $x\ –\ \frac{3}{x}\ =\ x^2$.
To do:
We have to check whether the given equation is quadratic.
Solution:
The standard form of a quadratic equation is $ax^2+bx+c=0$.
$x\ –\ \frac{3}{x}\ =\ x^2$
$x(x)-x(\frac{3}{x})=x(x^2)$ (Multiply by $x$ on both sides)
$x^2-3 = x^3$
$x^3-x^2+3=0$
The equation $x^3-x^2+3=0$ is not of the form $ax^2+bx+c=0$ as its degree is $3$.
Therefore, $x\ –\ \frac{3}{x}\ =\ x^2$ is not a quadratic equation.
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