(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) = x^4 - x^3 - 29x^2 - x - 30

Answer 1

P = +or- { 1,2,3,5,6,10,15,30}

f(-5) = 625 + 125 - 725 +5-30

= 750-725+5-30

= 0

-5 | 1 -1 -29 -1 -30

-5 30 -5 30

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1 -6 1 -6 0

x^3 - 6x^2 + x - 6 = 0

x^2(x-6) + (x-6) = 0

(x-6) (x^2 + 1) = 0

x = 6 or x = +or- i