Hey, my neighbour again send me one exercise.

1. In the equation $\displaystyle x^{3} - 7x^{2} - 21x + a = 0$ you must find solutions whose are in geometric sequence. For which $\displaystyle a$?

How can I find this $\displaystyle a$?

2. In the equation $\displaystyle x^{4} -(a+3)x^2 + (a + 2) = 0$ must find this $\displaystyle a$ that solutions are in arithmetic sequence.

How can I find this $\displaystyle a$?