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.
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.
Answer:
Let's think step by step.

user
-26
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.
train