how many different real roots does the equation x^4 + 3x^3 - 4x=0 have? thank you

Question

anonymous · Answer

x2-4x+3=(x-1)(x-3),. so the roots of the equation f(x)=0 are x=1 and x=3. Draw a ... Similarly, since f(2)<0, f(x) will be negative for all x in the interval (1,3). ... Here is another example: Find the solutions of the inequality ... Solve the equation f(x)=x2-3x+2=0. .... The polynomial x2+1 is irreducible, it does not have real roots.  @DavidxG

cwrw238 · Answer

x^4 + 3x^3 - 4x=0

x(x^3 + 3x2 - 4) = 0

so one of the real roots = 0

cwrw238 · Answer

x^3 + 3x^2 - 4 = 0

by inspection another root is  x = 1

cwrw238 · Answer

as its a quartic equation the maximum number of roots is 4 
- of which we have so far found 2.