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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.

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.

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter4: Polynomial And Rational Functions
Section4.1: Polynomial Functions Of Degree Greater Than
Problem 36E
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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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