Please help asap solve x^4+5x^2+4=0

Question

asked Jul 18, 2021 105k views

1 Answer

Learningtech · Answer 1 · 2021-07-22T13:46:41+0000

Answer:

$x=\pm i\text{ or }x=\pm2i$

Explanation:

So we have the equation:

x^4+5x^2+4=0

Let's let u be equal to x². So:

u^2+5u+4=0

Factor:

(u+1)(u+4)=0

Zero Product Property:

$u+1=0\text{ or } u+4=0$

Subtract:

$u=-1\text{ or }u=-4$

Replace:

$x^2=-1\text{ or }x^2=-4$

Take square root:

$x=\pm√(-1)\text{ or }x=\pm\sqrt{-4$

Simplify:

$x=\pm i\text{ or }x=\pm2i$