If the angles A , B , C are the solutions of the equations `tan^(3)-3ktan^(2)x-3tanx+k=0` , then the triangle ABC is

Options

A. isosceles
B. equilateral
C. acute angled
D. none of these

Explanation

Since A, B, C are the solutions of the equation
`tan^(3)x-3ktan^(2)x-3tanx+k=0`
`thereforetan A, tan B, tan C` are its roots.
`thereforetan A + tan B + tan C = 3k ,`
tan A tan B + tan B tan C + tan C tan A = - 3
and, tan A tan B tan C =-k
But, tan A + tan B + tan C = tan A tan B tan C
`therefore3k=-krArr4k=0rArrk=0`
`thereforetanAtanBtanC=0`
`rArr` tan A = 0 or, tan B = 0 or tan C = 0 which is not posssible.
Hence, such a triangle does not exist.