Why does an extraneous root get introduced?

​Extraneous Solutions occur because squaring both sides of a square root equation results in 2 solutions (the positive and negative number). Therefore, one of those numbers will be an extraneous solution, or an extra solution which does not fulfill the original equation.

Why do we need to check for extraneous solutions?

The reason extraneous solutions exist is because some operations produce ‘extra’ answers, and sometimes, these operations are a part of the path to solving the problem. When we get these ‘extra’ answers, they usually don’t work when we try to plug them back into the original problem.

What is an extraneous root of an equation?

An extraneous solution is a root of a transformed equation that is not a root of the original equation because it was excluded from the domain of the original equation. Example 1: Solve for x , 1x − 2+1x + 2=4(x − 2)(x + 2) .

What does extraneous root mean?

An “extraneous root” may be defined as “a value obtained. for an unknown in the solution of an equation which is not a. root of the equation.” It may be noted first that authors of.

Why do extraneous solutions sometimes occur in equation with rational expressions?

Why do extraneous solutions sometimes occur in the process of solving rational or radical equations? Answer: Squaring both sides of a square-root radical equation introduces two solutions (the positive and negative) that might be the solution to the equation.

What is meant by extraneous roots?

What is the meaning when having an extraneous solution?

Extraneous solutions are values that we get when solving equations that aren’t really solutions to the equation.

Why are trigonometric identities useful in solving equations?

Verifying the Fundamental Trigonometric Identities. Identities enable us to simplify complicated expressions. They are the basic tools of trigonometry used in solving trigonometric equations, just as factoring, finding common denominators, and using special formulas are the basic tools of solving algebraic equations.

What does it mean to solve a trigonometric equation?

Summary: A trigonometric equation is one that involves one or more of the six functions sine, cosine, tangent, cotangent, secant, and cosecant. Some trigonometric equations, like x = cos x, can be solved only numerically, through successive approximations.

What do you mean by extraneous roots or solution?

more A solution to an equation that SEEMS to be right, but when we check it (by substituting it into the original equation) turns out NOT to be right. Example: you work on an equation and come up with two roots (where it equals zero): “a” and “b”.

What is an extraneous solution to a rational function?

Rational Equation – An equation where one or more terms has x in the denominator. 1) Extraneous solution – An x-value that makes the equation undefined, or solutions that make any denominator equal to 0.