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# D1notes - Supplementary Course Module D Solving Equations...

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Assignment 1 ± Polynomial Equations An equation is a statement of equality between two expressions, and may involve one or more variables. A particular choice of value for the variable(s) which makes an equation true (i.e. the expression on the left hand side have a value equal to that of the expression on the right hand side) is called a solution or root of the equation; the collection of all solutions is called the solution set. ± x + 6 = 15 has solution x = 9 (i.e., its solution set is f 9 g ) ± the equation x 2 = 25 has two solutions, namely x = ± 5 (i.e., its solution set is 5 ; 5 g ) ± thus, the equation x 2 = ² 1 has no real solution (i.e., its solution set is ? ) Solving Polynomial Equations (of one variable) Isolating the variable using "opposite" operations: If all occurrences of the variable have the same power, then we can solve the equation by isolating the variable. We do this by applying the following principles. ± Addition Principle: Adding an expression which is defined everywhere to both sides of an equation yields an equivalent [ i.e., has exactly the same solution set ] equation. Wherever the added expression is undefined, the original equation must be checked. a = b , a + c = b + c , for all c 2 R ± Multiplication Principle: Multiplying an equation by an expression that is defined everywhere and never equal to zero yields an equivalent equation. Wherever the new expression is

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D1notes - Supplementary Course Module D Solving Equations...

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