Q. 336 - Intermediate Algebra

Question

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

Step-by-Step Solution

Answer

An example of such a quadratic equation is $2x^2-8=0$.

Step 1. Take a quadratic equation.

Let us take an example of a quadratic equation.

$2x^2-8=0 ...... \left(i\right)$

On rewriting, we see,

$\left(2\times x\times x\right)-\left(2\times 2\times 2\right)=0$

Here, the greatest common factor is $2$.

Step 2. Check if the solutions to the equation is zero.

On factoring equation (i),

$$\begin{gathered} 2\left(x^2-4\right)=0 \\ {x}^2-2^2=0 \\ \left(x-2\right)\left(x+2\right)=0 \end{gathered}$$

Use zero product property,

$$\begin{gathered} x-2=0 \\ x=2 \end{gathered}$$

Then,

$$\begin{gathered} x+2=0 \\ x=-2 \end{gathered}$$

Therefore, the only two solutions to this equation is $2,-2$.