<PRE><B>Question 94191</B>
Given x^3 - 4x^2 + 2x + 1 =0
(a)How many possible positive roots are there? 
(b)How many possible negative roots are there?
(c)What are the possible rational roots?
(d)Using synthetic substitution, which of the possible rational roots is 
   actually a root of the equation? 
(e)Find the irrational roots of the equation. (HINT: Use the quardratic      
   formula to solve the depressed equation.)
(a)_2 or 0 because f(x) has 2 changes of sign_
(b)_1 because f(-x) has one change of sign_
(c)_+1 or -1___________
(d)_x = 1___________
(e)_[3+sqrt13]/2 or [3-sqrt(13)]/2_   

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Using synthetic division with x=1 you get:
1)....1....-4....2....1
........1.....-3...-1..|..0

Quotient: x^2-3x-1
Using quadratic formula you get:
x=[3+-sqrt(9-4*1*-1)]/2
x=[3+-sqrt(13)]/2

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Cheers,
Stan H.


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