Thread: Rule of signs

Write the particular equation of a quartic function that could, according to Descartes Rule of Signs have four positive zeros.


Really not sure where to go with this. Do i just need to answer with the rule of signs...

Yes. Do you remember what "DesCartes rule of signs" says? If the coefficients of a polynomial, in order from highest power to lowest, or vice versa, change sign n times, then the maximum number of positive zeros the polynomial can have is n and may be less than n with the difference from n an even number- n-2, n- 4, n- 6 etc. So a polynomial, with four positive zeros must be of degree at least 4 and the coefficients must have at least four changes of sign.