State whether $6 x^{5} + 3 x^{2} - 7 = 0$ 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
The given equation is $6 x^{5} + 3 x^{2} - 7 = 0$ .
On comparing given equation with the standard form $a x^{2} + b x + c = 0$ , we can see that $a = 3$
However, the highest power of the variable $x$ is $5$ .
Hence, the equation $6 x^{5} + 3 x^{2} - 7 = 0$ is not a quadratic equation.

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