Question

Find all real numbers a such that the roots of the polynomial x^3 - 6x^2 + 21x + a
form an arithmetic progression and are not all real.

I don't know how to even start. Someone please help! Will medal and fan!

Answer 1

if roots in AP then they are b-d ,b,b+d

Answer 2

where b is first term and d is common difference

Answer 3

now find sum of roots ,product of roots and so on and compiar with quation.

Answer 4

if ax^3+bx^2+cx+d=0 is equation then sum of roots is=-b/a

Answer 5

so the sum of roots is -3b (where b in this case is the first term in the arithmetic series)?

Answer 6

compare your equation with std.one and which give value of a,b,c,d

Answer 7

okay thanks!

Answer 8

you understand it or not

Answer 9

i do