What are the solutions to P(x) = x4 + 2x3 + 6x2 - 3x - 7

Question

What are the solutions to  P(x) = x4 + 2x3 + 6x2 - 3x - 7

anonymous · Answer

use substitution 
let y = x^2 
now you would have 
p(y) = y^2 + 2y + 3-7
now combine the like terms and factor, or use quadratic equation

dumbcow · Answer

the only possible rational solutions are +-1, +-7  
if one of these works you can factor it out resulting in a cubic function....repeat until you get a quadratic

graphing it on a graphing calculator is also helpful :)

anonymous · Answer

@dumbcow I tested the factors +-1 and +-7 using synthetic division but none of them work.

dumbcow · Answer

that means solutions are irrational, unless you can factor the polynomial then only way to get solutions is by approximating using calculator or more complex methods involving calculus

anonymous · Answer

So will the solutions dhow up on a graph?

dumbcow · Answer

http://www.wolframalpha.com/input/?i=x%5E4+%2B2x%5E3+%2B+6x%5E2+-3x-7+%3D+0

anonymous · Answer

Because I have to describe a graph mainly focusing on the end behaviors and the x-intercepts but I can't find the solutions to the equation