(a) Determine the possible numbers of positive and negative real zeros of f and (b) list the possible rational zeros of f.

Question

f(x) = -3x^3 + 20x^2 - 36x + 16

Answer 1

P= +or- {1,2,4,8, 16}

Q = +or- {1,3}

P/Q = +or- {1,2,4,8,16,1/3,2/3, 4/3, 8/3, 16/3}

-3(2^3) + 20(2^2) - 36*2 + 16 = -24 + 80 - 72 + 16 = 0

2 | -3 20 -36 16

-6 28 -16

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-3 14 -8 0

-3x^2+14x-8 = 0

3x^2 - 14x-+8 = 0

(3x - 2)(x - 4 )=0

x = 2/3 x= 4