Letf(x), g(x) and h(x) be quadratic polynomials having positive leading coefficients and real and distinct roots. If each pair of them has a common root, then prove that the roots of f(x) + g(x) + h(x) = 0 are always real and distinct.

College Algebra (MindTap Course List)
12th Edition
ISBN:9781305652231
Author:R. David Gustafson, Jeff Hughes
Publisher:R. David Gustafson, Jeff Hughes
Chapter4: Polynomial And Rational Functions
Section4.CR: Chapter Review
Problem 61E
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Let f(x), g(x) and h(x) be quadratic polynomials having positive
leading coefficients and real and distinct roots. If each pair of
them has a common root, then prove that the roots of f(x) +
g(x) + h(x) = 0 are always real and distinct.
Transcribed Image Text:Let f(x), g(x) and h(x) be quadratic polynomials having positive leading coefficients and real and distinct roots. If each pair of them has a common root, then prove that the roots of f(x) + g(x) + h(x) = 0 are always real and distinct.
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