SOLUTION: What is the type and how many solutions are there to the following quadratic equation?
x^2-3x+3=0
A. one rational solution
B. two complex solutions
C. two rational solutions
T
Question 435483: What is the type and how many solutions are there to the following quadratic equation?
x^2-3x+3=0
A. one rational solution
B. two complex solutions
C. two rational solutions
Thanks. Answer by solver91311(24713) (Show Source):
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
John
My calculator said it, I believe it, that settles it
