Thread: Complex number equation

I need to determine what I can say about "c" if:

If c is a real number and you know that the equation
z^2 + 2z + c = 0 has at least one solution that is not real, what can you say about c?

I do not know that I have information to say anything about c, other than the fact that it is real as is stated. But, I know that z can not equal 0. Since we know it is the complex portion of this equation I guess that that is obvious. Are we able to conclude if c is greater than 1 or less than or equal to 1??? If so, please explain. Thank you! Frostking

Originally Posted by Frostking

I need to determine what I can say about "c" if:

If c is a real number and you know that the equation
z^2 + 2z + c = 0 has at least one solution that is not real, what can you say about c?

I do not know that I have information to say anything about c, other than the fact that it is real as is stated. But, I know that z can not equal 0. Since we know it is the complex portion of this equation I guess that that is obvious. Are we able to conclude if c is greater than 1 or less than or equal to 1??? If so, please explain. Thank you! Frostking

For a quadratic equation to have a non-real solution, the discriminant must be less than zero. Therefore ....