How do you solve #x^3 -3x^2 +16x -48 = 0#?

1 Answer
Feb 16, 2017

Answer:

#3 and +-i4#. See the Socratic graph of the cubic, making x-intercept 3..

Explanation:

From sign changes in the coefficients, the equation has utmost 3

positive roots,There are no changes in sign,

when x is changed to #-x#. And so, there are no negative roots.

The cubic is 0 at x = 0. So, it becomes

#(x-3)(x^2+16)#

The other solutions are from by #x^2+16=0#, giving #x =+-i4#

graph{(x-3)(x^2+16) [2, 4, -500, 500]} 0, -500, 500]}

Not to scale. It is large y vs small x, for approximating the solution.