SOLUTION: 1. find all the roots of x3+2x2+2x+1 2. if 2-i is a root of 3x3-11x2+11x+5, then what are its other roots? 3. find the negative root of x2-3+0 to the nearest tenth 4. how lo

Question 628470: 1. find all the roots of x3+2x2+2x+1
2. if 2-i is a root of 3x3-11x2+11x+5, then what are its other roots?
3. find the negative root of x2-3+0 to the nearest tenth
4. how long will it take a population with a 10% annual growth rate to double?
5. how many roots does x6=3x5+1 have?
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
1. find all the roots of x^3+2x^2+2x+1
Since f(-1) = 0, -1 is a root.
Use synthetic division to find other roots.
-1)....1....2....2....1
........1....1....1...|..0
Quotient: x^2+x+1
Use the quadratic formula:
x = [-1 +- sqrt(1-4*1*1)]/2 = [-1+-sqrt(-3)]/2 = (-1/2)+-isqrt(3)/2
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2. if 2-i is a root of 3x3-11x2+11x+5, then what are its other roots?
Since the coefficients are Real, 2+i is also a root.
Also x = -1/3 is a root.
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3. find the negative root of x^2-3+0 to the nearest tenth
Comment: Not an equation.
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4. how long will it take a population with a 10% annual growth rate to double?
Solve: 2P = p(1.1)^t
1.1^t = 2
t = log(2)/log(1.1) = 7.27 years
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5. how many roots does x6=3x5+1 have?
Ans: six
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Cheers,
Stan H.
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