Question

14. Write a quadratic equation that cannot be factored.

Answer 1

Given:

Quadratic equation

To write a quadratic equation that cannot be factored or cannot be solved by factoring, we note first that factoring is the easiest method to solve a quadratic equation as long as the equation is easily factorable. If not, we'll need alternative approaches like employing the quadratic formula.

We also note that factoring cannot always be used to solve quadratic equations.

Below is an example of an equation that can be solve by factoring:

`\begin{gathered} x^2-3x-10=0 \\ (x-5)(x+2)=0 \end{gathered}`

Now, the equation that cannot be factored or cannot be solved by factoring is:

`x^2+x-1=0`

We cannot apply factoring to the above equation. Therefore, the answer is:

`x^2+x-1=0`