SOLVING POLYNOMIAL EQUATIONS USING RATIONAL ROOT THEOREM WORKSHEET

Problem 1 :

Solve the equation

x3 - 5x2 - 4x + 20 = 0

Solution

Problem 2 :

f(x) = 3x4 - 2x2 + 6x - 10

Solution

Problem 3 :

f(x) = x3 - 10x2 + 14x - 36

Solution

Problem 4 :

f(x) = x3 + 3x2 - x + 8

Solution

Problem 5 :

f(x) = 5 - 7x4 + 3x2 + x -20

Solution

Problem 6 :

f(x) = x4 - 7x3 - 4x2 + x - 49

Solution

Problem 7 :

f(x) = 2x4 - 5x3 + 8x2 + 3x - 5

Solution

Problem 8 :

f(x) = 3x4 - 5x3 + 10x + 12

Solution

Problem 9 :

f(x) = 4x5 - 2x + 18

Solution

Problem 10 :

f(x) = 5x6 - 3x4 + 5x3 + 2x2 - 15

Solution

Answer Key

1)  three solutions of the given cubic polynomial is {-2, 2, and 5}.

2)   ±1, ±2, ±5, ±10, ±1/3, ±2/3, ±5/3, ±10/3

3)  ±1, ±2, ±3, ±4, ±6, ±9, ±12, ±18, ±36

4)  ±1, ±2, ±4, ±8

5)   ±1, ±3, ±1/7, ±3/7, ±5/7, ±15/7

6)  ±1, ±7, ±49

7)  ±1, ±5, ±1/2, ±5/2

8)  ±1,±2, ±4, ±6, ±12, ±1/3, ±2/3, ±4/3

9)  ±1,±2, ±3, ±12, ±1/2, ±1/4, ±3/2, ±3/4, ±9/2

10)  ±1, ±3, ±5, ±15, ±3/5

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