Question 619026: x^2+8x+20=0
i dont know if these are complex numbers but the problem says solve the equation in the complex number system Answer by solver91311(24713) (Show Source):
ALL numbers are in the complex number system. Real numbers just happen to have an imaginary part coefficient of zero.
Use the discriminant to determine the nature of your roots:
For any quadratic polynomial equation of the form:
Find the Discriminant, and evaluate the nature of the roots as follows:
No calculation quick look: If the signs on and are opposite, then guaranteed.
Two real and unequal roots. If is a perfect square, the quadratic factors over (the rationals).
One real root with a multiplicity of two. That is to say that the trinomial is a perfect square and has two identical factors. Presuming rational coefficients, the root will be rational as well.
A conjugate pair of complex roots of the form where is the imaginary number defined by
For your problem, 64 - 80 = -16, so
Go right from here to the quadratic formula:
From here just simplify. Your two zeros will have the form
John
My calculator said it, I believe it, that settles it
