The equation has one real root and two complex roots of the form and where are real numbers. Find a+b
I'm not sure where to begin. I don't understand how to solve these kinds of expressions. Sometimes can group terms and find a way to factor the polynomial so that the roots are obvious. I don't understand how his would work if some of the roots were complex numbers. Would the equation take the form:
I don't understand even understand how to use the theorem, nor do I understand why it works.
Rational root theorem - Wikipedia, the free encyclopedia
In the example on the wikipedia page, it seems that they just took the 2 and 3 in the equation: to get , but where did the come from?
I was thinking about finding the point of inflection by the second derivative test to find a root. Is it true that the point of inflection of a cubic function will always be on the x-axis, and will thus give us the real root?