Question

State whether $x(x+1)+8=(x+2)(x-2)$ 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 $x(x+1)+8=(x+2)(x-2)$ in standard form.

$$\begin{gathered} x(x+1)+8=(x+2)(x-2) \\ \Rightarrow x^2+x+8=x^2-4 \\ \Rightarrow x+12=0 \end{gathered}$$

On comparing this equation with the standard form $a{x}^2+bx+c=0$, we can see that $a=0$.

However, the highest power of the variable $x$ is $1$.

Hence, the equation $x(x+1)+8=(x+2)(x-2)$ is not a quadratic equation.