Given f(x) = 2x^4-3x^3-10x^2+12x+8
1. Use Descarte's Rule of Signs to determine the possible number of negative and positive real roots and the number of complex roots. ( I do not know how to do this)
2. Use the rational roots theorem to find all possible rational roots (zeros)
+1, -1, +2, -2, +4, -4, +8, -8, +1/2, -1/2 (Is this correct? I found by ratio p/q)
3. Find all real and complex roots. (Real roots found by graphing -2, 2, -1/2. How to find complex roots?I factored the function: f(x)= (x-2) (x+2) (2x^2-3x-2). Then I solved the quadratic part by using quadratic formula: x=2 and x=-1/2. The initial function can be factored: (x-2)^2 (x+2) (x+1/2). Is this correct? How to find complex zeros? Does it have complex zeros?
Thank you very much for your help.