SOLUTION: The equation 2x^4 − 3x^3 − 14 x^2 − 22x − 8 = 0 has two real and two complex solutions. What is the product of the two complex solutions?

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: The equation 2x^4 − 3x^3 − 14 x^2 − 22x − 8 = 0 has two real and two complex solutions. What is the product of the two complex solutions?      Log On


   



Question 252309: The equation 2x^4 − 3x^3 − 14 x^2 − 22x − 8 = 0 has two real and two complex
solutions. What is the product of the two complex solutions?

Answer by drk(1908) About Me  (Show Source):
You can put this solution on YOUR website!
Let's look at this using Descartes rule of signs. X = 4 and X = -2 will generate roots.
X = 4 divides the original polynomial with an answer of: 2X%5E3+%2B+5X%5E2+%2B+6X+%2B+2
X = -1/2 divides the second polynomial with an answer of: 2X%5E2+%2B+4X+%2B+4+
Set this polynomial = 0 and use quadratic. We get X = -1+%2B-+isqrt%282%29