SOLUTION: 2 different rational solutions, 2 different irrational solutions,exactly one rational solution or 2 different imaginary solutions?? x^2

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Question 234430: 2 different rational solutions, 2 different irrational solutions,exactly one rational solution or 2 different imaginary solutions??
x^2 - 12x + 34 = 0
Answer by solver91311(24713) (Show Source):
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Calculate the discriminant:

, where , , and are the lead, 1st degree, and constant coefficients of the quadratic equation in standard form. Then:

Two real and unequal roots. If the discriminant is a perfect square, then the roots are rational, otherwise they ar e irrational.

One real root with a multiplicity of two. That is to say that the trinomial is a perfect square and has two identical factors.

A conjugate pair of complex roots of the form where is the imaginary number defined by

John

SOLUTION: 2 different rational solutions, 2 different irrational solutions,exactly one rational solution or 2 different imaginary solutions?? x^2 - 12x + 34 = 0