Question

Find all roots. Name the type of roots and how many.
x^4 + 5x^2 - 36=0

Answer 1

2 and 3i

Explanation:

Let's find the answer to this problem using something called u-substitution. This means that we can replace x^2 with some variable u, and rewrite the equation:

`u^2+5u-36=0`

Now this is a typical quadratic equation that you know how to solve:

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

`u=4,-9`

`x^2=4,-9`

This problem has two roots,
`√(4)=2` and
`√(-9)=3i` (not sure if you guys are allowed to use imaginary numbers yet). Hope this helps!