Complex Roots: Solving for the Number and Identification

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SUMMARY

The equation 18x² + 3x - 1 = 0 has two complex roots. The quadratic formula is the recommended method for solving this equation, as factoring proves ineffective. The polynomial can be factored as (6x - 1)(3x + 1), confirming the roots are real rather than complex. The discussion highlights a common misunderstanding regarding the terminology of "complex roots" in relation to this specific problem.

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Homework Statement


State the number of complex roots and then identify what the roots are.

Equation:
18x^2 + 3x -1 = 0


Homework Equations





The Attempt at a Solution


There are 2 complex roots.

Okay. So I can't factor anything out of the equation and when you try to factor it by hand it doesn't work. So what should I do? quadratic formula? Please help me.
 
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I would use the quadratic formula, yes.
 
Yes, quadratic formula.
 
thanks.
 
You can factor out the polynomial as
18x^2 + 6x - 3x - 1
= 6x(3x+1) - (3x+1)
= (6x-1) (3x+1)
 
I wish you would stop titling these "complex roots". So far none of the problems you have posted has had complex roots!
 
oh sorry. In my book that section says "complex roots" but next time I will try my best to label it appropriately.
 

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