Question

Statement-I Given equation `x^6-12x^5+ax^4+bx^3+cx^2+dx+64=0` has six positive roots `a_i(i=1,2,......6)` then the value of `|a+b|=100` Statement-II For the equation `x^6-12x^5+ax^4+bx^3+cx^2+dx+64=0` with six positive roots `a_i(i=1,2...6). `a=sum a_i a_2 and b=- suma_1 a_2 a_3`.

Answer 1

`alpha_!+alpha_2+alpha_3+alpha_4+alpha_5+alpha_6=12`
`alpha_1alpha_2alpha_3alpha_4alpha_5alpha_6=64`
`AM=12/6=2`
`GM=(64)^(1/6)=2`
`AM=GM`
`alpha_1=alpha+2=alpha_3=alpha_4=alpha_5=alpha+6=2`
`a=6C_2*4=60`
`b=-6C_3*6=-160`
`|a+b|=100`
option 1 is correct.