You need to be more specific. A quadratic equation will have 2 solutions. The 2 solutions can be equal (such as x² + 2x + 1 = 0, solution is -1 and -1). If one of the solutions is a real number, then the other solution will also be a real number. If one of the solutions is a complex number, then the other solution will also be a complex number. [a complex number has a real component and an imaginary component]
In the equation: Ax² + Bx + C = 0. The term [B² - 4AC] will determine if the solution is a double-root, or if the answer is real or complex.
if B² = 4AC, then a double-root (real).
if B² > 4AC, then 2 real roots
if B² < 4AC, then the quadratic formula will produce a square root of a negative number, and the solution will be 2 complex numbers.
If B = 0, then the numbers will be either pure imaginary or real, and negatives of each other [ example 2i and -2i are solutions to x² + 4 = 0]
Example of 2 real and opposite sign: x² - 4 = 0; 2 and -2 are solutions.
There are three kinds:the equations have a unique solutionthe equations have no solutionthe equations have infinitely many solutions.
The three types of linear equations are: Consistent Dependent, Consistent Independent, and Inconsistent.
Let the number of unknowns be N. The solution space may have N, N-1, ..., 0 dimensions or may not exist. If a solution exists and the dimension of the solution space is 0, then there is exactly one solution,. If the dimension of the solution space > 0, then there are infinitely many solutions.
Three different kinds: none, one and infinitely many.
the 5 kinds of factoring are common monomial factor, difference of two cubes, quadratic trinomial, perfect square trinomial,and difference of two square.
The answer depends on the nature of the equation. Just as there are different ways of solving a linear equation with a real solution and a quadratic equation with real solutions, and other kinds of equations, there are different methods for solving different kinds of imaginary equations.
There are three kinds:the equations have a unique solutionthe equations have no solutionthe equations have infinitely many solutions.
There are many kinds of differential equations and their solutions require different methods.
The Two kinds of Solution are:SolventSolute
The three types of linear equations are: Consistent Dependent, Consistent Independent, and Inconsistent.
The answer will depend on what kinds of equations: there are linear equations, polynomials of various orders, algebraic equations, trigonometric equations, exponential ones and logarithmic ones. There are single equations, systems of linear equations, systems of linear and non-linear equations. There are also differential equations which are classified by order and by degree. There are also partial differential equations.
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Let the number of unknowns be N. The solution space may have N, N-1, ..., 0 dimensions or may not exist. If a solution exists and the dimension of the solution space is 0, then there is exactly one solution,. If the dimension of the solution space > 0, then there are infinitely many solutions.
Real numbers, imaginary numbers and irrational numbers are three kinds of numbers. Others are rational numbers, algebraic numbers and primes numbers. There are many more.
the kinds of solutions are saturated and saturated.
solutions, colloids and suspensions
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