Let P(x) = ax² +bx+c with a 0. The polynomial P(x) is factorable in real numbers if we can find real numbers m, n, k and I so that P(x) = (mx+n) (kx + 1). a) Show that P(x) is factorable if and only if b2 - 4ac > 0. b) Show that 3x² 5x+10 is not factorable in real numbers. -

Let P(x) = ax² +bx+c with a 0. The polynomial P(x) is factorable in real numbers if we can find real numbers m, n, k and I so that P(x) = (mx+n) (kx + 1). a) Show that P(x) is factorable if and only if b2 - 4ac > 0. b) Show that 3x² 5x+10 is not factorable in real numbers. -

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter4: Polynomial And Rational Functions

Section4.4: Complex And Rational Zeros Of Polynomials

Problem 38E

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Question

Answer using mathematical proof

Let P(x) = ax² +bx+c with a ‡0. The polynomial P(x) is factorable in real numbers if we
can find real numbers m, n, k and I so that P(x) = (mx +n)(kx+1).
a) Show that P(x) is factorable if and only if 6²
4ac > 0.
b) Show that 3x² - 5x + 10 is not factorable in real numbers.

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