Solve for x x5 6x4 x3 24x2 20x greaterthanorequalto 0Sol

Solve for x: x^5 - 6x^4 + x^3 + 24x^2 - 20x greaterthanorequalto 0

Solution

2)

let f(x)=x^5 -6x^4 +x^3+24x^2-20x

x^5 -6x^4 +x^3+24x^2-20x=0

factors of constant -20 are ±1,2,4,5,10,20, factors of leading coefficient 1 are ±1

possible rational zeros are ±(1,2,4,5,10,20) _/±1

x^5 -6x^4 +x^3+24x^2-20x=0 for x =-2,0,1,2,5

sign table:

x..............-2.............0.............1...........2.............5.....................

f(x).....(-).........(+)...........(-)...........(+)...........(-)...........(+)..........

so solution for x^5 -6x^4 +x^3+24x^2-20x>=0 is [-2,0]U[1,2]U[5,)