Rational Zero Theorem (topics 8.6)

One: Find all the zeros of the function f(x) = x3 – 17x2 + 81x – 65.

Two: Find all of the zeros of the function f(x) = 6x3 – 76x2 + 256 – 256.

Three: List all of the possible rational zeros of the following function.

f(x) = 2x6 – 5x5 – 25x4 + 66x3 + 20x2 – 13x + 9

Four: List all of the possible rational zeros of the following function.

f(x) = x6 – 7x5 – 24x4 + 64x3 + 20x2 – 20x + 100

Five: Find all the rational zeros of the function f(x) = 2x(4) – 6x(3) – 106x(2) – 18x.

Six: Find all the rational zeros of the function f(x) = 24 x(4) + 44x(3) – 12x(2) – 8x.

Seven: Find all the rational zeros of the function f(x) = 48x(4) + 88x(3) – 24x(2) – 16x.

 

Answers (  ONE:  1, (8 – i), (8 + i)   TW0: 25, 50,O:  2.67, 2, 8   THREE: plus or minus (1, 3, 9, 1/2, 3/2, 9/2)   FOUR: plus or minus (1, 2, 4, 5, 10, 2 100)  FIVE:  0, 9   SIX: 1/2, 0, -1/3, -2   SEVEN: the same, why? )

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