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It means that some equations can have more than one solution, and that you are supposed to find all of them. For example, equations with polynomials tend to have more than once solution; thus, x squared = 25 is satisfied both for x = 5, and for x = -5.

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Give a general expression that encompasses all possible answers, or give each root of an equation

Q: What does all solutions mean when solving an algebraic equation?

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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.

You just wrote the verbal equation. Do you mean the algebraic equation? X - 4 = - 12 ---------------

That is what roots mean!

It means it is not an algebraic number. Algebraic numbers include square roots, cubic roots, etc., but more generally, algebraic numbers are solutions of polynomial equations.

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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.

You just wrote the verbal equation. Do you mean the algebraic equation? X - 4 = - 12 ---------------

That is what roots mean!

Real but not a root of an algebraic equation with rational roots coefficients

It means it is not an algebraic number. Algebraic numbers include square roots, cubic roots, etc., but more generally, algebraic numbers are solutions of polynomial equations.

The discriminant tells you how many solutions there are to an equation The discriminant is b2-4ac For example, two solutions for a equation would mean the discriminant is positive. If it had 1 solution would mean the discriminant is zero If it had no solutions would mean that the discriminant is negative

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It has infinitely many solutions.

The set of all the solutions of an equation or condition

It is an algebraic expression but if you mean 5x-4y-28 = 0 then it is a straight line equation.

Solving a one variable linear equation involves getting the variable on one side of the equals sign by itself. To do this one uses the properties of numbers.

If you mean: x2+8x-9 = 0 then the solutions are x = 1 and x = -9