# Thread: Polynomials and Imaginary numbers

1. ## Polynomials and Imaginary numbers

How do I solve questions such as P(x) = 16x^4 - 81

Am I not allowed to use the Quadratic Formula? Are there any conditions to using the Quadratic Formula? Thanks

2. Originally Posted by JonathanEyoon
How do I solve questions such as P(x) = 16x^4 - 81

Am I not allowed to use the Quadratic Formula? Are there any conditions to using the Quadratic Formula? Thanks
Hint: difference of two squares

and that's just one option, i actually see another way to solve it. you want to find P(x) = 0 right? equate P(x) to 0 and get the x on one side. it's easier than you think, there are no middle terms to bug us

3. Originally Posted by Jhevon
Hint: difference of two squares

and that's just one option, i actually see another way to solve it. you want to find P(x) = 0 right? equate P(x) to 0 and get the x on one side. it's easier than you think, there are no middle terms to bug us

(4x^2 + 9)(4x^2 - 9)

May I ask what's the other way

4. Originally Posted by JonathanEyoon
(4x^2 + 9)(4x^2 - 9)
yes, that's very good! now you notice that what's in the second pair of brackets is also the difference of 2 squares, and what's in the first pair has two imaginary solutions

May I ask what's the other way
Nevermind. I tried it, i ended up with something very similar, but i wasn't able to get the imaginary solutions. the above method is best. continue

5. Originally Posted by Jhevon
yes, that's very good! now you notice that what's in the second pair of brackets is also the difference of 2 squares, and what's in the first pair has two imaginary solutions

Nevermind. I tried it, i ended up with something very similar, but i wasn't able to get the imaginary solutions. the above method is best. continue

Thanks~!!