SOLUTION: One of the roots of the cubic equation x^3-4x^2+2x+4=0 is A. 1+ the square root of 3 B. -1+ the square root of 3 C. -1+2 the square root of 3 D. 1+2 the square root of 3

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons  -> Quadratic Equation Lesson -> SOLUTION: One of the roots of the cubic equation x^3-4x^2+2x+4=0 is A. 1+ the square root of 3 B. -1+ the square root of 3 C. -1+2 the square root of 3 D. 1+2 the square root of 3      Log On


   

Question 308764: One of the roots of the cubic equation x^3-4x^2+2x+4=0 is
A. 1+ the square root of 3
B. -1+ the square root of 3
C. -1+2 the square root of 3
D. 1+2 the square root of 3
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
One of the roots of the cubic equation x^3-4x^2+2x+4=0 is
A. 1+ the square root of 3
B. -1+ the square root of 3
C. -1+2 the square root of 3
D. 1+2 the square root of 3
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I graphed the equation and found a zero at x = 2
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Now use synthetic division to find the other zeroes:
2)....1....-4....2....4
.......1.....-2...-2..|..0

Solve x^2-2x-2 = 0
x = [2 +- sqrt(4-4*1*-2)]/2
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x = [2 +- sqrt(12)]/2
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x = [2 +- 2sqrt(3)]/2
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x = 1+sqrt(3) or x = 1-sqrt(3)
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Cheers,
Stan H.