Question

State whether $\frac{3x}{4}-\frac{5x^2}{8}=\frac{7}{8}$ is a quadratic equation.

Answer 1

Step 1: Definition of a quadratic equation

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

For a given equation to be a quadratic equation,$a\ne 0$ 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 $\frac{3x}{4}-\frac{5x^2}{8}=\frac{7}{8}$ in standard form.

$$\begin{gathered} \frac{3x}{4}-\frac{5x^2}{8}=\frac{7}{8} \\ \Rightarrow \frac{6x-5x^2}{8}=\frac{7}{8} \\ \Rightarrow 6x-5x^2=7 \\ \Rightarrow 5x^2-6x+7=0 \end{gathered}$$

On comparing this equation with the standard form $a{x}^2+bx+c=0$, we can see that, $a=5$ and the highest power of the variable $x$ is $2$.

Hence, the equation $\frac{3x}{4}-\frac{5x^2}{8}=\frac{7}{8}$ is a quadratic equation.