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| Symmetric Functions |
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| Any expression f(a,b) involving two numbers a and b is said to be symmetric if it remains unchanged when a and b are interchanged. |
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| [i.e. if f(a,b) = f(b,a)]. |
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| Some of the symmetric functions of a and b are |
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| All symmetric functions of a and b can be expressed in terms of two symmetric functions a+b and ab. |
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| For instance, |
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| We thus observe, without actually solving the quadratic equation |
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| (a) We can find the value of every symmetric function involving the roots of the equation in terms of the coefficients of the equation. |
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| (b) We can find a quadratic equation whose roots are any one of the following pairs of numbers. |
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| where a and b are the roots of the given equation. |
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