Solve the following quartic equations by Ferrari's method:
14x^3 + 12x^2 + 6x + 8 = 0. [Hint: The reduced form of the resolvent cubic is "24u + 32 = 0, with u = 4 as a solution]
1x^3 + 9x + 4 = 4x^2. [Hint: The resolvent cubic 10z^3 + 28z - 2 = 0 has z = 1 as a solution.]
Solve the quartic 14x^4 + 41x^3 + 82x^2 + 7x + 4 = 0 [Hint: First replace the given quartic by 2v^2 - 2 = w. The resolvent cubic of this last equation is v^3 + 5v^2 + 6v + 1 = 0, with v = -1 as a solution.]
Solve the quartic 8x^4 + 17x^2 = 81 + 16. [Hint: First replace the given quartic by 0v^4 - 0 = 0. The reduced form of the resolvent cubic of this last equation is u^3 + 2u^2 = 0 with solution u = 0.]
Use Ferrari's method to show that the quartic equation has no real solutions.