Have you tried the sum and products of roots?
Given roots and in the cubic equation
In the cubic equation the constants p and q are real and is a root. I want to find the other two roots but I'm a little lost at what to do to get one of them.
I know that is a root as the conjugate is always a root, and I also know that a cubic equation has either one or three real roots - so it follows that the other root I need to find is real.
I tried finding the sum and product of the roots but I can't because I don't know what p and q are yet - I tried using an algebraic division method but the same can be said for this, and I don't know any other method to get the other root.
The second part of the question asks to find the values of p and q, but I take it that there's a way to get the other root without getting these first? Could anyone suggest a method?
Thanks if you can help me out
Also, I presume you know that a cubic, with leading coefficient 1, is equal to where , and are the roots. You know that one root is 2+ 3i and another is 2- 3i. That tells you that this can be written as for some real number . Multiplying, . Now you know that . I would make a "wild guess" at being 26/13= 2!.
And once you know that it is easy to find p and q.
I tried finding the sum and product of the roots but I can't because I don't know what p and q are yet - I tried using an algebraic division method but the same can be said for this, and I don't know any other method to get the other root.
The second part of the question asks to find the values of p and q, but I take it that there's a way to get the other root without getting these first? Could anyone suggest a method?
Thanks if you can help me out