Question

Give an example of a quadratic equation that has a GCF and none of the solutions to the equation is zero.

Short answer

$2x^2-2=0$

Step-by-step solution

Step 1. Given information

A quadratic equation is an equation of degree two , meaning the highest component of this function is two.

Step 2. Example

An equation that has a GCF and none of the solutions to the equation is zero is $2x^2-2=0$.

As on factoring,

$$\begin{gathered} 2x^2-2=0 \\ 2x^2=2 \\ {x}^2=\frac{2}{2} \\ {x}^2=1 \\ x=\sqrt{1} \\ x=\pm 1 \end{gathered}$$

Step 3. Solution

As solutions are $\pm 1$, so none of them are zero.

Also GCF is same i.e.$1$.