Let v and w be distinct, randomly chosen roots (real or complex) of the equation `z^(9)-1=0` .The probability that `1<=|v+w|` is 1/k, then "k" is equal to

The number of real roots of the equation z^(3)+iz-1=0 is

Prove that the equation Z^(3)+iZ-1=0 has no real roots.

Three distinct vertices are randomly chosen among the vertices of a cube. The probability that they from equilateral triangle is

Let a,b and c be three real and distinct numbers.If the difference of the roots of the equation ax^(2)+bx-c=0 is 1, then roots of the equation ax^(2)-ax+c=0 are always (b!=0)

If f(x)=x^(3)-3x+1, then the number of distinct real roots of the equation f(f(x))=0 is

If the roots of the equation ax^(2)+bx+c=0 are real and distinct,then

If p and q are chosen randomly from the set {1,2,3,4,5,6,7,8,9,10} with replacement, determine the probability that the roots of the equation x^(2)+px+q=0 are real.

A term of randomly chosen from the expansion of (root(6)(4) + 1/(root(4)(5)))^(20) . If the probability that it is a rational term is P, then 420P is euqal to