rational root theorem

Question

Rational root theorem for :

1. need the possible zeros and the solutions
2. f(x)=x^4-10x^2+9=0
3. f(x)= x^4-10x^2+9=0
4. f(x)= 3x^3-4x^2-5x+2=0

Answer 1

Problems 1 and 2 are the same.

1. Possible zeros are: Factors of 9/factors of 1 = ±1,±3,±9

It can be solved by factoring (x²-9)(x²-1) = (x+3)(x-3)(x+1)(x-1)

Solving we get the zeros: -3,3,-1,1

2. Possible zeros are: Factors of 2/Factors of 3 = ±2,±2/3,±1,±1/3

We can test using synthetic division or graphing and find the actual zeros: -1,1/3,2