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
Algebra.Com
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): You can put this solution on YOUR website!
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
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