Question

8. If all the zeroes of a cubic polynomial
x3 + ax? - bx + c are positive, then what can you say
about a, b and c?​

Answer 1

Step-by-step explanation:

Let the roots of the equation x3+ax2+bx+c=0 be α,β,γ

Then, sum of roots, α+β+γ=−a. Thus, a is negative.

Product of roots, taken two at a time, α.β+α.γ+γ.β=b. Thus b is positive

Product of roots, α.β.γ=−c. Thus c is negative.

Hence, a and c have -ve sign, but b has +ve sign.