can you help me answer this in hand writing please? Suppose f(x) = x² + 3x + 1. In this problem, we will show that f has exactly one root (or zero) in theinterval [-4, –1].(a) First, we show that f has a root in the interval (-4,-1). Since f is a choosefunctionon the interval [-4, –1] and f(-4) =and f(-1) =, the graphof y = f(x) must cross the r-axis at some point in the interval (-4, –1) by thechoosev. Thus, f has at least one root in the interval [-4, –1].(b) Second, we show that f cannot have more than one root in the interval [-4, –1] by a thoughtexperiment. Suppose that there were two roots x = a and æ = b in the interval [-4, –1] with a

Answered: Image /qna-images/answer/6b39a79f-9aa9-4ca2-9f9e-470c7be1050e.jpg

Suppose f(x) = r² + 3x + 1. In this problem, we will show that f has exactly one root (or zero) in the interval [-4, –1). (a) First, we show that f has a root in the interval (–4, –1). Since f is a choose function on the interval [-4, –1] and f(-4) = of y = f(x) must cross the x-axis at some point in the interval (–4, –1) by the and f(-1) = , the graph choose v. Thus, f has at least one root in the interval [–4, –1]. (b) Second, we show that f cannot have more than one root in the interval [-4, –1] by a thought experiment. Suppose that there were two roots a = a and a = b in the interval [-4, –1] with a < b. Then f(a) = f(b) = Since f is choose v on the interval [-4, – 1] and choose on the interval (-4, –1), by choose there would exist a point c in interval (a, b) so that f' (c) = 0. However, the only solution to f' (x) = 0 is x = which is not in the interval (a, b), or in [–4, –1]. Thus, ƒ cannot have more than one roet in

Suppose f(x) = r² + 3x + 1. In this problem, we will show that f has exactly one root (or zero) in the interval [-4, –1). (a) First, we show that f has a root in the interval (–4, –1). Since f is a choose function on the interval [-4, –1] and f(-4) = of y = f(x) must cross the x-axis at some point in the interval (–4, –1) by the and f(-1) = , the graph choose v. Thus, f has at least one root in the interval [–4, –1]. (b) Second, we show that f cannot have more than one root in the interval [-4, –1] by a thought experiment. Suppose that there were two roots a = a and a = b in the interval [-4, –1] with a < b. Then f(a) = f(b) = Since f is choose v on the interval [-4, – 1] and choose on the interval (-4, –1), by choose there would exist a point c in interval (a, b) so that f' (c) = 0. However, the only solution to f' (x) = 0 is x = which is not in the interval (a, b), or in [–4, –1]. Thus, ƒ cannot have more than one roet in

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter4: Polynomial And Rational Functions

Section4.5: Rational Functions

Problem 54E

See similar textbooks