Question

please help! x^4-x^3-2x-4=0
how do i solve the equation by first finding the rational roots?

Answer 1

possible roots are +-1, +-2, +-4

Answer 2

then i found the roots -1 and 2 by synthetic division, how do i find the third/fourth root?

Answer 3

factor, you will have a quadratic left, use the quadratic formula

Answer 4

i have two quadratics left from -1 and 2. which one do i use?

Answer 5

you know what i means by factor? you said -1 is a root, so \[x^4-x^3-2x-4=(x+1)(\text{some cubic})\]

Answer 6

you can find the cubic by synthetic division

Answer 7

then from the cubic expression factor out the other root \(x-2\) so you will have \[x^4-x^3-2x-4=(x+1)(x-2)(\text{some quadratic})\]

Answer 8

perhaps you can factor the quadratic, but you can always set that equal to zero and solve via the quadratic formula

Answer 9

I'll try solving it

Answer 10

It works. Thank you!
So this is the method for solving any question like this?

Answer 11

yes

Answer 12

you should have got \(x^2+2\) for the quadratic

Answer 13

my final answer is {-1,2, +-sqrt2i}