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How do you find the roots of and equation?
The roots of an equation means the solutions of an equation. Different methods have been developed for different kinds of equation. It is not possible to give an overview in one or two paragraphs, but in simpler cases, the same operation is done on both sides of the equation, with the aim of "isolating" the variable you are solving for, that is, having it alone on one side. In some complicated cases, no "explicit" solutions exist, and "numerical" solutions have to be used; this basically means using trial-and-error.
The result of solving and equation is called the?
The result of solving an equation is called the solution. It is the value or set of values that satisfy the equation, making both sides equal when substituted into it. In the context of algebra, solutions can be numbers, variables, or expressions that fulfill the given mathematical condition.
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 method is used for solving a rational equation?
Methods vary considerably depending upon the number of powers in the equation. For example, the method for solving cubics is quite different to solving quadratics etc... It's not really possible to generalise to one technique.
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.
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.
Is satisfying an equation the same as solving it?
No. If an equation has many solutions, any one of them will satisfy it.
Which step would not be a possible first step for solving the following equation algebraically?
The first step not possible in solving an equation algebraically is not to provide an equation in the first place in which it appears to be so in this case.
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 do you find the roots of and equation?
The roots of an equation means the solutions of an equation. Different methods have been developed for different kinds of equation. It is not possible to give an overview in one or two paragraphs, but in simpler cases, the same operation is done on both sides of the equation, with the aim of "isolating" the variable you are solving for, that is, having it alone on one side. In some complicated cases, no "explicit" solutions exist, and "numerical" solutions have to be used; this basically means using trial-and-error.
Solving quadratic equation by completing the square?
Yes it is quite possible
Holistic problem solving?
Holistic problem solving is solving a problem from all possible aspects. This will cover all the details of the problem and the relevant solutions.
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 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 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.
