Quadratics, even those with complex number solutions, can be solved using the discriminant, and square roots. Practice this with polynomials, and...
After you complete the quiz, move on over to the corresponding lesson titled How to Solve Quadratics with Complex Numbers as the Solution. The lesson covers these objectives: Understand the discriminant Relate the discriminant to the solutions Explore the square roots of negative numbers ...
For what value of kk will kx2+x+k=0kx2+x+k=0 have two real solutions? The answer key says −1/2<k<1/2−1/2<k<1/2, yet when I tried k=0k=0 in the equation, I received only one solution of x=0x=0. However, the discriminant with k=0k=0, is still greater than ...
For ordinary differential equations in the complex domain, a central problem is to understand, in a given equation or class of equations, those whose solutions do not present multivaluedness. We consider autonomous, first-order, quadratic homogeneous equations in three variables, and begin the class...
Can have two solutions, no solution, or one solution 7 Compare with Definitions Linear Involves a constant rate of change. The cost increases linearly with the number of items purchased. 9 Quadratic Features a squared variable, introducing curvature. The area of a square can be modeled by a ...
The necessary and sufficient conditions for the existence and the explicit expression for the general solution are obtained for the quadratic matrix equation X*AX+B*X+D=0, where A∈Cn×n,B∈Cn×p and D∈Cp×p are given complex matrices with D*=D and A*=A, and (·)* denotes the ...
subtraction, multiplication, and division. For example, the scalars may becomplex numbers, or they may be elements of a finite field such as the field having only the two elements 0 and 1, where 1 + 1 = 0. The coordinates of a vector are scalars, and when these scalars are from the...
That is, for any convex norm Φ, de Weger gives a number ∆(Φ) for which 1 |P − Qα|p ≤ ∆(Φ)Φ(P, Q)2 has infinitely many solutions for α∈ Q, and any p, but for which only finitely many solutions exist for sufficiently large p when ∆(Φ) is replaced by a...
The design goal of this library was to create a simple, yet powerful, not too bogus math tool that scientists and developers could deploy with their work to solve mathematical problems both simple and complex. ParserNG is written completely in (pure) Java and so is as cross-platform as Java...
periodic solutionsharmonic balancebifurcation analysischaosThe paper deals with the characterization of Hopf bifurcations in families of simple nonlinear systems, i.e., third-order autonomous systems with few nonlinear terms. By employing Harmonic Balance (HB) tools, the complete set of system parameters...