If the equation `x^(4)-4x^(3)+ax^(2)+bx+1=0` has four positive roots, find the values of a and b.

Answer

6

Explanation

`x^(4)-4x^(3)+ax^(2)+bx+1=0`
let root are `alpha,beta,gamma&lamda`
`=alpha+beta+gamma+lamda=4`
`alphabetagammalamda=1`
As all roots are positive
`=a.m.gtg.m`
`=(alpha+beta+gamma+lamda)/(4)gt(alphabetagammalamda)^((1//4))`
all the numbers are equal
`alpha=beta=gamma=lamda`
`alpha+beta+gamma+lamda=4`
`implies4alpha=4impliesalpha=1`
`alpha=beta=gamma=lamda=1`