Complex Conjugate Roots of a Cubic - Cardon's Method
Can you show me how to work this? Is there only one way and what is most acceptable?
Find the values of the complex conjugate roots for the equation x^3 + 3X^2 +2 = 0.
Solution Summary
Detailed step-by-step procedure of using Cardon's method to determine the roots of a cubic equation.
An elliptic curve can be written as y^2=x^3+ax+b. I need a proof for why x^3+ax+b either have 3 real roots or 1 real root and 2 complexroots. I don't have anything that I know about it prior to asking for help here at Brainmass.
The equation x^4 - 18x^3 + 121x^2 - 368x + 420=0
has complexconjugateroots (4+j2) & (4-j2). By a process of division and solving a quadratic equation, find all the roots and hence write down all the factors of :
x^4
1 Find the real and complex solutions of these cubic equations.
a) (z-3)(z2-5z+8)=0
b) z3 - 10z2- 34z- 40 = 0, given that 3-i is a root (solution).
2 Solve the equation z3 = 125 cis 45
3 Consider the complex number: z =
= cos + z sin
a) Use De Moivre's theorem to find z2, z4 and z6. Leave your answers in polar form.
b) Pl
Determine if the following have a solution or not? justify answer.
(apply the discriminant) are the roots real, repeated real, or complex?
1) 5x^2+8x+7=0
2) (7)^1/2y^2-6y-13(7)^1/2=0
3) 2x^2=x-1=0
4) 4/3x^2-2x+3/4=0
5) 2x^2+5x+5=0
6) p^2-4p+4=0
7) m^2=m+1=0
8) 3z^2+z-1=0
Determine if the following equations are real or complex; explain the answer in detail.
Determine whether the following equations real or complex solutions; justify your answer. Note: It is not necessary to find the solutions; just determine if they are real or complex and explain why.
a) 5x2 + 8x + 7 = 0
b) (7)1/2y2 - 6
Prove that if p is a polynomial with real coefficients, and if is a (complex) solution of P(E)z = 0, then the conjugate of z, the real part of z, and the imaginary part of z are also solutions.
Note: This is from a numerical analysis course, and here P(E) refers to a polynomial in E, the "shift operator" for a sequence.
Exercise. IV. This problem is a partial investigation of which n×n matrices over C have
cube roots; that is, for which n × n matrices A over C there is an n × n B over C such
that A = B3. Since C is algebraically closed, every n × n matrix over C is similar over C
to a matrix in Jordan canonical form.
A. Suppose that A
