What are the solutions of the equation x4 – 5x2 – 36 = 0? Use factoring to solve. x = ±2 and x = ±3 x = ±2i and x = ±3 x = ±2 and x = ±3i x = ±2i and x = ±3i

Question

asked Sep 25, 2021 110k views

2 Answers

Dqthe · Answer 1 · 2021-10-01T13:00:53+0000

Answer:

$x=\pm 3\text{ or } x=\pm 2i$

Explanation:

So we have the equation:

x^4-5x^2-36=0

Let's let u equal x² so:

u^2-5u-36=0

Factor. We can use -9 and 4. So:

u^2+4u-9u-36=0

From the first two terms, factor out a u.

From the last two terms, factor out a -9. So:

u(u+4)-9(u+4)=0

Grouping:

(u-9)(u+4)=0

Zero Product Property:

$u-9=0 \text{ or } u+4=0$

On the left, add 9. On the right, subtract 4:

$u=9\text{ or } u=-4$

Substitute back u:

$x^2=9\text{ or } x^2=-4$

Take the square root:

$x=\pm 3\text{ or } x=\pm 2i$

And we're done!

Our answer is the Second option.