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How do you know when an Equation has an infinity solutions without solving the equation?
Wiki User
∙ 10y ago
You can't really know that in all cases. But with some practice in working with equations, you'll start to notice certain patterns. For example, you'll know that certain functions are periodic, and that an equation such as:
sin(x) = 0
have infinitely many solutions, due to the periodicity of the function. This one is easy; we can make some small changes:
sin(2x + 3) = 0.5
Here it isn't as easy to guess the exact solutions of the equation, but due to our knowledge of the periodicity of the sine function, we can assume that it has infinitely many solutions.
Another example: a single equation with two or more variables normally has infinitely many solutions, for example:
y = 3x + 2
Wiki User
∙ 10y ago
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How can you tell how many solutions a quadratic equation will have without solving it?
A quadratic equation can have a maximum of 2 solutions. If the discriminant (b2-4ac) turns out to be less than 0, the equation will have no real roots. If the Discriminant is equal to 0, it will have equal roots. But, if the discriminant turns out to be more than 0,then the equation will have unequal and real roots.
What does extraneous mean What must you do to determine whether a solution is an extraneous solution?
Extraneous means extra and unnecessary. Extraneous solutions are values that can arise from the process of solving the equation but do not in fact satisfy the initial equation. These solutions occur most often when not all parts of the process of solving are not completely reversible - for example, if both sides of the equation are squared at some point.
What role of operations that applies when you are solving an equation does not apply when your solving an inequality?
What role of operations that applies when you are solving an equation does not apply when your solving an inequality?"
What is s solving an equation?
An equation is a mathematical statement that may (or may not) be true, defined for some variables. Solving an equation is finding those values of the variables for which the equation or statement is true.
How is solving an equality the same as solving an equation?
An equality and equation are essentially the same thing. The equality between two expressions is represented by an equation (and conversely).
Is satisfying an equation the same as solving it?
No. If an equation has many solutions, any one of them will satisfy it.
Is it possible to have imaginary solutions when solving a polynomial equation?
yes
When solving a rational equation why is it necessary to perform a check?
It is important to check your answers to make sure that it doesn't give a zero denominator in the original equation. When we multiply both sides of an equation by the LCM the result might have solutions that are not solutions of the original equation. We have to check possible solutions in the original equation to make sure that the denominator does not equal zero. There is also the possibility that calculation errors were made in solving.
How is solving an inequality different from solving an equation?
In solving an inequality you generally use the same methods as for solving an equation. The main difference is that when you multiply or divide each side by a negative, you have to switch the direction of the inequality sign. The solution to an equation is often a single value, but the solution to an inequality is usually an infinite set of numbers, such as x>3.
How would you go about solving a quadratic equation?
Write the quadratic equation in the form ax2 + bx + c = 0 then the roots (solutions) of the equation are: [-b ± √(b2 - 4*a*c)]/(2*a)
What happens if you are checking a solution for the radical expression and find that it makes one of the denominators in the expression equal to zero?
Then it is not a solution of the original equation. It is quite common, when solving equations involving radicals, or even when solving equations with fractions, that "extraneous" solutions are added in the converted equation - additional solutions that are not solutions of the original equation. For example, when you multiply both sides of an equation by a factor (x-1), this is valid EXCEPT for the case that x = 1. Therefore, in this example, if x = 1 is a solution of the transformed equation, it may not be a solution to the original equation.
How do you solve imaginary equations?
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.
In general when solving a radical equation should you first isolate the radical and then both sides?
It often helps to isolate the radical, and then square both sides. Beware of extraneous solutions - the new equation may have solutions that are not part of the solutions of the original equation, so you definitely need to check any purported solutions with the original equation.
What is the result of solving an equation?
It is the solution of the equation
What is a solution set?
is a set of all replacements that make an equation time in mathematics solution set is set of values which satisfies a given equation. For solving solutions you can get help from online Find Math Solutions.
How would you know that your equation has no solutions without actually solving it?
It really depends on the type of equation. Sometimes you can know, from experience with similar equations. But in many cases, you have to actually do the work of trying to solve the equation.
Can a math problem have more than one answer?
Yes, it can. For example, if you are solving a quadratic equation, the curve could cross the x-axis in more than one place, thus the equation would have two solutions, a cubic equatuion can have 3 solutions, an equation with a power of four in it can have four solutions, etcetera.
