## tien.lam12 3 years ago What are the possible number of positive, negative, and complex zeros of f(x) = -3x4 - 5x3 - x2 - 8x + 4 ? A) Positive: 2 or 0; Negative: 2 or 0; Complex: 4 or 2 or 0 B) Positive: 1; Negative: 3 or 1; Complex: 2 or 0 C) Positive: 3 or 1; Negative: 1; Complex: 2 or 0 D) Positive: 4 or 2 or 0; Negative: 2 or 0; Complex: 4 or 2 or 0

1. ChukRock

the numbers after the x's are exponents, correct?

2. tien.lam12

yes

3. joeywhite

there are 2 positive and 2 complex roots

4. joeywhite

i've tried using descartes rule of signs but i got confused to be honest so i solved it

5. sahil51993

one root lie b/w 0 and 1

6. joeywhite

right

7. sahil51993

other will be negative as f(x) is increasing in R+

8. sahil51993

Am i right????

9. joeywhite

no 2 positive

10. sahil51993

yeah 1 will be positive and one will not be possitive it can also be possilbe that roots may be irrational becuase irrational roots also exist in pairs

11. estudier

there is 1 sign change so by DRS there is 1 positive root Sub -x for x to get negative roots, 3 sign changes so 3 or 1 negative roots Complex roots are total roots, 4, less positive and negative roots so 0 or 2 of those. Answer is B