2015/042) If roots of the equation $x^4 - 8x^3 + bx^2 +cx +16 =0$ are positive ,then?

a) b=8=c
b)c= -32, b=28
c)b=24,c= -32
d)c=32, b=24


Product = 16 and sum = 8 and all are >0

they are $2,2,2,2$ other combinations for example $(1,1,1,16)$ , $(1,1,2,8)$ do not give sum 8

so the expression is $(x-2)^4$

= $x^4-8x^3 + 24x^2 - 32x + 16$

hence $b = 24$ and $c = - 32$