Question

State whether $(x+1)(x+3)=0$ 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 $(x+1)(x+3)=0$ in standard form.

$$\begin{gathered} (x+1)(x+3)=0 \\ \Rightarrow x(x+3)+1(x+3)=0 \\ \Rightarrow x^2+3x+x+3=0 \\ \Rightarrow x^2+4x+3=0 \end{gathered}$$

On comparing this equation with the standard form $a{x}^2+bx+c=0$, we can see that $a=1$ and the highest power of the variable $x$ is $2$.

Hence, the equation $(x+1)(x+3)=0$ is a quadratic equation.