Question

I have to use Rational Root Theorem to find all possible rational roots of the following 3x^3+2x^2+x-4=0. Please help.

And find all roots for:
2x^5-4x^4-15x^3+22x^2+25x-30=0

Answer 1

let f(x)=3x^3+2x^2+x-4
let x=p/q be a solution of the equation
to have a list of possible rational roots of the equation we should know all the divisors of 3 and -4 ! so p is a divisor of -4 and q is divior of 3 !
then \[x \in { \pm1;\pm 2; \pm \frac{2}{3}}\]
I think 1 is good ,so you can find polynomial function g wich satisfies f(x)=(x-1)g(x) g(x) will be in this form g(x)=ax^2+bx+c so try to solve g(x)=0 with the quadratic formula !