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1. Solve the following polynomial inequalities, xER. a) x² - 4x +3<0 b) x²-3x-220 c) x-120

1. Solve the following polynomial inequalities, xER. a) x² - 4x +3<0 b) x²-3x-220 c) x-120

College Algebra (MindTap Course List)
College Algebra (MindTap Course List)
12th Edition
ISBN:9781305652231
Author:R. David Gustafson, Jeff Hughes
Publisher:R. David Gustafson, Jeff Hughes
Chapter1: Equations And Inequalities
Section1.8: Absolute Value
Problem 92E
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Practice 1. Solve the following polynomial inequalities, xER. x² - 4x+3<0 x³-3x-2≥0 x-1≥0 1²3x+10 - 2x² - 2x³ +16x² +24x<0 12[x=3|=_=1)² (F=5750 a) b) g) h) i) -3(x+4)(x-3) >0 x¹ <22x² +75 2x² - 2x ≥2-x 2. Let f(x)=-2x+1, g(x) = x² - 2x +1 and h(x)= x³ -1. Determine all values of x such that f(x) < g(x) <h(x) and paste the struation graphically. 3. The number n (in hundreds), of mosquitoes in a camping area after t weeks can be modelled by the equation n(t) = 2t -5t³ -16t² +45t .According to this model, when will the population of mosquitoes be greater than 1800? 4) A zo6 wishes to construct an aquarium in the shape of a rectangular prism such that the length is twice the width/and/5 m greater than the height. If the aquarium must have a volume strictly betwee een 1125 m³ and 3000 m³, determine the restrictions on the length of the aquarium. 5. Determine the equation of a quintic function f(x) that satisfies the following conditions: o f(-3)=f(0) = S(4)=0 o ƒ(1)=-9 o f(x) > 0 whenx<-3 or-3<x<0 o f(x) <0when 0<x<4orx>4 Illustrate the situation graphically. 6. The solution to x² +bx+24 <0 is the set of all values of x such that k<x<k+2 for some real value of k. Determine all possible values of b, bER. Justify your answer. 7. A quartic function has turning points at (-3,0),(1,0), and (-1,-16). Determine all values of x such that -9<f(x) <0. 6| Page
Transcribed Image Text:Practice 1. Solve the following polynomial inequalities, xER. x² - 4x+3<0 x³-3x-2≥0 x-1≥0 1²3x+10 - 2x² - 2x³ +16x² +24x<0 12[x=3|=_=1)² (F=5750 a) b) g) h) i) -3(x+4)(x-3) >0 x¹ <22x² +75 2x² - 2x ≥2-x 2. Let f(x)=-2x+1, g(x) = x² - 2x +1 and h(x)= x³ -1. Determine all values of x such that f(x) < g(x) <h(x) and paste the struation graphically. 3. The number n (in hundreds), of mosquitoes in a camping area after t weeks can be modelled by the equation n(t) = 2t -5t³ -16t² +45t .According to this model, when will the population of mosquitoes be greater than 1800? 4) A zo6 wishes to construct an aquarium in the shape of a rectangular prism such that the length is twice the width/and/5 m greater than the height. If the aquarium must have a volume strictly betwee een 1125 m³ and 3000 m³, determine the restrictions on the length of the aquarium. 5. Determine the equation of a quintic function f(x) that satisfies the following conditions: o f(-3)=f(0) = S(4)=0 o ƒ(1)=-9 o f(x) > 0 whenx<-3 or-3<x<0 o f(x) <0when 0<x<4orx>4 Illustrate the situation graphically. 6. The solution to x² +bx+24 <0 is the set of all values of x such that k<x<k+2 for some real value of k. Determine all possible values of b, bER. Justify your answer. 7. A quartic function has turning points at (-3,0),(1,0), and (-1,-16). Determine all values of x such that -9<f(x) <0. 6| Page
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