Complex Roots: Solving for the Number and Identification

In summary, the equation 18x^2 + 3x - 1 = 0 has 2 complex roots. To solve for these roots, the quadratic formula can be used or the polynomial can be factored as (6x-1)(3x+1). However, the term "complex roots" may be misleading in this context as the solutions are not actually complex numbers.
  • #1
Corkery
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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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  • #2
I would use the quadratic formula, yes.
 
  • #3
Yes, quadratic formula.
 
  • #4
thanks.
 
  • #5
You can factor out the polynomial as
18x^2 + 6x - 3x - 1
= 6x(3x+1) - (3x+1)
= (6x-1) (3x+1)
 
  • #6
I wish you would stop titling these "complex roots". So far none of the problems you have posted has had complex roots!
 
  • #7
oh sorry. In my book that section says "complex roots" but next time I will try my best to label it appropriately.
 

1. What is "Another Complex root problem"?

Another Complex root problem refers to a mathematical problem where the solutions or roots of a given equation involve complex numbers, which are numbers that contain both real and imaginary components.

2. How do complex roots differ from real roots?

Complex roots differ from real roots in that they involve imaginary numbers, which cannot be plotted on a traditional number line. Real roots, on the other hand, are numbers that can be plotted on a number line.

3. Why are complex roots important?

Complex roots are important because they allow us to find solutions to equations that would otherwise have no real solutions. They also have many applications in fields such as engineering, physics, and computer science.

4. How are complex roots typically represented?

Complex roots are typically represented in the form a + bi, where a and b are real numbers and i is the imaginary unit (defined as the square root of -1).

5. Can complex roots be solved using traditional methods?

Yes, complex roots can be solved using traditional algebraic methods, such as the quadratic formula or factoring. However, the solutions will involve complex numbers instead of real numbers.

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