Unformatted text preview: why f ( a,b,c,d ) is a real number. (Hint: The Fundamental Theorem of Symmetric Functions.) A.3. Let a,b,c,d be the roots of some real quartic equation with no x 3 term (i.e. we have a + b + c + d = 0.) Let p = a + b , q = a + c , and r = a + d , so thatp = c + d ,q = b + d , andr = b + c . Prove that pqr is a real number, and hencep 2 q 2 r 2 is a negative real number. (Hint: Show that pqr is invariant under permuting a ↔ b , or a ↔ c , or a ↔ d . Hence it’s invariant under any permutation of a,b,c,d .)...
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 Spring '11
 Armstrong
 Algebra, Addition, Factors, Quadratic equation, Complex number, Euler, real quartic equation

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