Question 94191This question is from textbook
: 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)____________
(b)____________
(c)____________
(d)____________
(e)____________
This question is from textbook
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! 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_
====================
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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