SOLUTION: Hello, I need help solving the following inequalities using algebra. These questions contain imaginary numbers. x^2+4x+8<0 x^2+1>&#8805;0 I can get the answer for x, but

Algebra ->  Inequalities -> SOLUTION: Hello, I need help solving the following inequalities using algebra. These questions contain imaginary numbers. x^2+4x+8<0 x^2+1>&#8805;0 I can get the answer for x, but       Log On


   

Question 1039815: Hello, I need help solving the following inequalities using algebra. These questions contain imaginary numbers.
x^2+4x+8<0
x^2+1>≥0
I can get the answer for x, but don't know where to go from there to get the solution and interval notation.
Thanks!
Answer by josgarithmetic(39621) About Me  (Show Source):
You can put this solution on YOUR website!
x%5E2%2B4x%2B8%3C0

If put as a graph for y=x%5E2%2B4x%2B8, and you check were y%3C0,
graph%28400%2C400%2C-10%2C5%2C-5%2C10%2Cx%5E2%2B4x%2B8%29
you understand that for real numbers, no solution.

You can solve the original inequality for Complex numbers, and use Completing the Square in the process. Look for your lessons on that. You would find within the solution, an expression, 4%5E2-4%2A1%2A8, your inequality's discriminant.

D for discriminant,
D=16-32
D=-16

Roots are x=%28-4%2B-+sqrt%28-16%29%29%2F2
x=%28-4%2B-+4i%29%2F2
x=-2%2B-+2i
...and your solution is for x BETWEEN these roots. The trouble with that is, complex numbers do not have order. NO SOLUTION.