Math..Find the rational roots of the following...?

Question

a)2x^4-4x^3-3x^2-x-3=0
b)6x^4+5x^3-x^2+x+1=0
c)x^4-3x^3+3x^2+x-6=0
d)2x^4+3x^3-3x^2+4=0

2)How do you graph polynomial functions like this:
a) f(x)=-x^3+2x^2+4x-8
b)f(x)=x^3-6x-9

Answer 1

If f(x) = (a_n)x^n + (a_(n-1))x^(n-1) + ... + (a_1)x + a_0 has a rational root r/s, then r is a divisor of a_0 and s is a divisor of a_n.

For example, for your first problem, rational roots r/s will have r = +/-1 or +/-3 and s = +/-1 or +/-2. Therefore, the possible rational roots are 1, -1, 3, -3, 1/2, -1/2, 3/2, -3/2. Try each one of the possibilities.

Note: A polynomial need not have any rational roots; the roots may all be irrational or complex. For example, the equation x^4 - x^2 - 2 = 0 has no rational roots.