If a₀ , a₁ , a₂ , a₃ , are all positive , then 4a₀x³ + 3a₁x² + 2a₂x + a₃ = 0 has at least one root in (-1,0) if
a: a₀ + a₂ = a₁ + a₃ and 4a₀ + 2a₂ > 3a₁ + a₃
b: 4a₀ + 2a₂ < 3a₁ + a₃
c: a₀ + a₂ > a₁ + a₃ and 4a₀ + 2a₂ = 3a₁ + a₃
d: a₀ + a₂ > a₁ + a₃ and 4a₀ + 2a₂ < 3a₁ + a₃

If , then you have




By the intermediate value theorem, there will be some number such that (i.e. will have a root in ) if you can guarantee that or .

Since the coefficients are all positive, then you know right away that , so you need to have in order for there to be such a .

This means you need to have



which means (A) must be the answer.