What are the possible number of positive, negative, and complex zeros of f(x) = 3x4 – 5x3 – x2 – 8x + 4 ?

Question

anonymous · Answer

Positive: 2; Negative: 2; Complex: 4 or 2 or 0

 Positive: 1; Negative: 3 or 1; Complex: 2 or 0

 Positive: 3 or 1; Negative: 1; Complex: 2 or 0

 Positive: 2 or 0; Negative: 2 or 0; Complex: 4 or 2 or 0

unklerhaukus · Answer

so its a forth degree function, ie a quartic function, 
$$f(x) = 3x^4 – 5x^3 – x^2 – 8x + 4$$

unklerhaukus · Answer

the coefficient of the main term is positive so as x gets really large in magnitude, 
the curve will be positive

anonymous · Answer

oh, so does that mean the complex will be 4?

unklerhaukus · Answer

i dont know the answer im trying to work it out

unklerhaukus · Answer

$$f(0)=4$$
so the y intercept is going to be 4

unklerhaukus · Answer

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unklerhaukus · Answer

$$f(1)<0$$
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