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Quadratic Equations

State whether...

Question

State whether $3 x + \frac{1}{x} - 8 = 0$ is a quadratic equation.

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Solution

Step 1: Definition of a quadratic equation
The standard form of a quadratic equation is $a x^{2} + b x + c = 0$ .
For a given equation to be a quadratic equation, $a \neq 0$ . and the highest power of the variable in the equation should be $2$ .
Step 2: To check whether the equation is a quadratic equation
Writing the given equation $3 x + \frac{1}{x} - 8 = 0$ in standard form of quadratic equation.
$\begin{array}{rcl} 3 x + \frac{1}{x} - 8 & = & 0 \\ \Rightarrow & 3 x^{2} + 1 - 8 x = 0 \\ \Rightarrow & 3 x^{2} - 8 x + 1 = 0 \end{array}$
On comparing this equation with the standard form $a x^{2} + b x + c = 0$ , we can see that $a = 3$ and the highest power of the variable $x$ is $2$ .
Hence, the equation $3 x + \frac{1}{x} - 8 = 0$ is a quadratic equation.

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