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17. Find all the roots of the equation.

x3 - 2x2 - x + 2 = 0

No roots 0, -1

-1, 1, 2 -1

18. Find all roots of the equation

x3 - x2 - 14x + 24 = 0

-4, 2, 3 4, 2, 3

0, 4 -4, 3

19. Find all roots of the equation

6y5 - 13y4 - 6y3 + 17y2 - 4 = 0

-1, -0.5, 2/3, 1, 2 1, 0.5, 2/3, -1, -2

-1, 0.5, 1, 2 0, -1, -0.5, 2/3, 1, 2

20. Find all the zeros of the polynomial

(x + 1)(x - 4)(x2 - 7)

-1, 4 -1, 4, ±Ö 7

No zeros 0

21. Find all zeros of the polynomial

x3 - 5x2 + x - 5

5, i -5, -i

0, 1 5, ± i

22. Find all rational roots of:

x5 - 2x4 + 11x3 - 22x2 - 12x + 24 = 0

1, -1 1, -1, 2

0, 1, 2 i, -i, 1, 2

23. Use the Rational Roots Theorem to solve the equation for the rational roots

x3 - 3x2 + 4x - 12 = 0

-3, 0 4, 12, 3

3 3, ± 2i

24. Use the Rational Roots Theorem to solve the equation for the rational roots

x4 - 2x3 - 8x2 + 10x + 15 = 0

No rational roots i, -2i

-1, 3 1, -3

25. Use the Rational Roots Theorem to solve the equation for the rational roots.

4y5 + 8y4 - 29y3 - 42y2 + 45y + 54 = 0

-3, 2, -1, ± 1.5 -3, 1.5, -1

2, -1.5, -1, 3 8, -2, 3, 1.5

26. Use the Rational Roots Theorem to solve for the rational roots

3x4 - 2x3 + 8x2 - 6x - 3 = 0

-1/3, 1, -i -1/3, 1

1/3, -1 1, i

27. Use the Rational Roots Theorem to solve for the rational roots

8y4 - 6y3 + 17y2 - 12y + 2 = 0

0.25, 0.5 0.25, 0.5, ± i

-0.25, -0.5, -i -0.25, -0.5

28. Find all the roots of the equation:

P(x) = 0.25x2 - 12x + 23

2, 46 2, 11

3, 4/5 -1, 7

29. Find all roots of the equation

3x2 - 11x - 4 = 0

-3, 4 3, 4

-1/3, 4 4

I'd like to help you with this but it looks like a homework problem. Is there something that you just don't understand about finding roots using the Rational Root Theorem that I can help with? May be working an example in detail. If you truly do understand this approach (perhaps with my help), then you should be able to do the problems fairly easily. They would be tedious and boring maybe, but you could do them (sort of the like long division).

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college mathematics, applied math, advanced calculus, complex analysis, linear and abstract algebra, probability theory, signal processing, undergraduate physics, physical oceanography

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