Question

What are the solutions of the equation x4 – 5x2 – 14 = 0? Use factoring to solve.

Answer 1

Answer:

$x=\pm 7\text{ or } x=\pm i\sqrt{2}$

Step-by-step explanation:

We have the equation:

$x^4-5x^2-14=0$

Since this is in quadratic form, we can consider using u-substitution. Thus, we will let:

$u=x^2$

Then by substitution:

$u^2-5x-14=0$

Now we can solve normally. Factor:

$(u-7)(u+2)=0$

Zero Product Property:

$u=7\text{ or } u=-2$

Back-substitute:

$x^2=7\text{ and } x^2=-2$

Take the square root of both sides. Since we are taking an even-root, we will need to add plus-minus:

$x=\pm 7\text{ and }x=\sqrt{-2}$

Therefore, our solutions are:

$x=\pm7\text{ and } x=\pm i\sqrt{2}$