# How do I do these 3 math problems? (college algebra)?

(that is, one root of the equation is listed below, find another root)

a.) 6 – 5i

b.) 18 + 7i

and also how can I find all the roots for this:

P(x) = 2x^3 – 2x^2 – 3x – 1= 0

Favorite Answer

a) and b) are solved in the same way. We know the coefficients of the polynomial are real which means the complex roots (if there are any) must occur in pairs with equal real and opposite imaginary parts. Why is this?

Well, let’s say the roots (zero points) of a polynomial are at x= a, b, c, … then if we write down the expression (x-a)(x-b)(x-c) … and multiply it all out, it gets us right back to the polynomial. In other words a polymonial expression is completely and uniquely defined by its roots. (sorry to seem patronising if you appreciate this already but, if you don’t, it probably seems a bit wierd – anyway it’s a big part of the usefulness of polymonials in science and engineering and it’s the reason why we’re so fascinated by these roots).

So now we come to the reason for the form of complex roots. When we muliply out all the brackets in the polynomial the imaginary parts must cancel out otherwise we’d get complex coefficients. In order to do this they must occur in pairs like a+ib and a-ib (try multiplying it out yourself – you will see that the imaginary parts in the coefficients disappear) so if you know that one of your roots is 6-5i then there must be another root equal to 6+5i and likewise 18+7i must have a compliment in 18-7i. That’s it.

To find the roots of a cubic equation I believe there is a formula but for higher polynomials than that I never knew of one so I’d often use the following simple method:

Make a sketch of the y=polynomial curve by filling in a few values of x and plotting them against the resulting y values on a sheet of paper. This gives you a fair idea where the roots are (values of x where the curve crosses the x axis). In this case there are roots around 1.9, -0.6 and -1.2 very approximately. Using a calculator or better a small programme in Excel to evaluate the polynomial, you can iterate (fool around) with x values until you hit zero as accurately as you want. That’s the root.

I hope this helped,

Bramble

use the quadratic equation but make it equal to x^2

so X^2=(-b+-squrt b^2-4ac)/2a

- Academic Writing
- Accounting
- Anthropology
- Article
- Blog
- Business
- Career
- Case Study
- Critical Thinking
- Culture
- Dissertation
- Education
- Education Questions
- Essay Tips
- Essay Writing
- Finance
- Free Essay Samples
- Free Essay Templates
- Free Essay Topics
- Health
- History
- Human Resources
- Law
- Literature
- Management
- Marketing
- Nursing
- other
- Politics
- Problem Solving
- Psychology
- Report
- Research Paper
- Review Writing
- Social Issues
- Speech Writing
- Term Paper
- Thesis Writing
- Writing Styles