SOLUTION: Now discuss this quadratic equation and determine the number and nature of the solutions, using the determine whether the solutions are real or complex? 3x^2 - 2x - 1 = 0

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equation Customizable Word Problems -> SOLUTION: Now discuss this quadratic equation and determine the number and nature of the solutions, using the determine whether the solutions are real or complex? 3x^2 - 2x - 1 = 0      Log On


   

Question 331078: Now discuss this quadratic equation and determine the number and nature of the solutions, using the determine whether the solutions are real or complex?
3x^2 - 2x - 1 = 0
Answer by solver91311(24713) About Me  (Show Source):
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For any quadratic polynomial equation of the form:



For your quadratic:

, , and

Find the Discriminant, and evaluate the nature of the roots as follows:


Two real and unequal roots. If is a perfect square, the quadratic factors over .

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

My calculator said it, I believe it, that settles it