Question

How do you solve this?

54x^5-60x^4+16x^3+90x^2-38x=0

Answer 1

Looks like those all have common factors, try factoring stuff out and seeing if anything jumps out at you.

Answer 2

try putting it to wolframalpha :)
http://www.wolframalpha.com/input/?t=crmtb01&f=ob&i=54x%5E5-60x%5E4%2B16x%5E3%2B90x%5E2-38x%3D0

Answer 3

@Kainui the answers seem to be... a bit... weird... or even... don't... ex... ist...?

Answer 4

Define "exist". @kc_kennylau

Answer 5

well for this kind of problems the answers must be... inte... gers... i mean... rational?

Answer 6

How would you solve this without graphing or using the calculator?

Answer 7

The answer in simple: No, you wouldn't.

Answer 8

@christianawilmett

You'd solve it by factoring out all the common factors. For instance, everything is multiplied by x, you can factor that out. How about 2? Is there anything else? So clearly if you plug in 0, that will be one of your factors. But you have to keep going with it... I don't feel like you're trying, but I'll help you figure it out if you are. Show me some work.

Answer 9

In details: https://en.wikipedia.org/wiki/Galois_theory

Answer 10

Hahahahaha you're going to link someone to Galois theory? Get real @kc_kennylau and instead of linking people to random articles all the time actually work on giving real advice and help rather than just googling random stuff to throw at people, cause you're mostly wasting your time.

Answer 11

@Kainui that's what "exist"s

Answer 12

"Imaginary" numbers aren't any less real than the normal real numbers you're used to. Did you ever think that maybe all numbers are really imaginary?

The complex number system really just extends the idea of a number line into a number plane. Imaginary numbers are just as legitimate and real as any other number. If you don't believe i "exists" then what's the square root of negative one?

Answer 13

But if this is used as an academic question, the roots would not be... well... you know... eh... kinda... yeah...

Answer 14

Academic question? What? That's something made up in your own mind. Complex roots as answers show up in schools.

Answer 15

just look at my photo that's the real roots

Answer 16

"Real" numbers aren't any more real than "imaginary" numbers. They're both equally as real, and complex numbers are probably even more real in reality.

Answer 17

ok if you can work out the roots (the roots are in my picture) in the exam, then nvm

gtg bye :)

Answer 18

Thatnk you!