SOLUTION: Given the polynomial function f(x), find the rational zeros, then the other zeros (that is, solve the equation f(x) = 0) : f(x) = x^3-4x^2+9x-10

Question 633044: Given the polynomial function f(x), find the rational zeros, then the other zeros (that is, solve the equation f(x) = 0) : f(x) = x^3-4x^2+9x-10
Answer by lwsshak3(11628) (Show Source): You can put this solution on YOUR website!
Given the polynomial function f(x), find the rational zeros, then the other zeros (that is, solve the equation f(x) = 0) : f(x) = x^3-4x^2+9x-10
**
use rational roots theorem to solve:
....0....|.......1........-4..........9.........-10
....1....|.......1........-3..........6.........-4
....2....|.......1........-2..........5...........0 (2 is a root or zero)
f(x)=(x-2)(x^2-2x+5)=0
x-2=0
x=2
..
x^2-2x+5=0
a=1, b=-2, c=5
discriminant=b^2-4ac=4-4*1*5<0
..
Function has one real root at x=2, and a pair of non-real or imaginary roots
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