Question

how do you find the roots of c^3-7C^2+16C-12=0

Answer 1

Let a=12-c^3
Solve a - 16 C + 7 C^2 = 0 for C. Replace a with 12-c^3 and simplify.\[\left\{C=\frac{1}{7} \left(8-\sqrt{-20+7 c^3}\right),C=\frac{1}{7} \left(8+\sqrt{-20+7 c^3}\right)\right\} \]

Answer 2

how did you know what to set a as?

Answer 3

or actually I see how you knew that...but your answers still have cs in them. How do you get rid of those?

Answer 4

I have to leave in a minute.
Pick a c and the corresponding values for C can be computed. There are restrictions on the values for c. Refer to the attachment from Mathematica.