Holt Mcdougal Larson Algebra 2: Student Edition 2012
1st Edition
ISBN: 9780547647159
Author: HOLT MCDOUGAL
Publisher: HOLT MCDOUGAL
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Expert Solution & Answer
Chapter 2.6, Problem 22E
Solution
To find: all real zeros of the function.
The real zeros of the function 23,2, and 4 .
Given information:
The f(x)=−3x3+20x2−36x+16 .
Formula used:
The Rational Zero Theorem:
If f(x)=anxn+⋯+a1x+a0 consists of integer coefficients, then the shape of each rational zero of f is as follows:
pq= factor of constant term a0 factor of leading coefficient an
Calculation:
Consider the function
f(x)=−3x3+20x2−36x+16
List the possible rational zeros of f :
±11,±21,±41,±81,±161,±13,±23,±43,±83,±163
Choose reasonable values from the list above to check using the graph of the function.
For f , the values x=23,x=2 and x=4 are reasonable based on the graph.
Check the values using synthetic division until a zero is found.
23 is a zero.
23−320−3616−212−16−318−240
Factor out a binomial using the result of the synthetic division.
Write a product of factors.
Factor −3 out of the second factor.
Multiply the first factor by −3 .
(x−23)(−3x2+18x−24)(x−23)(−3)(x2−6x+8)(−3x+2)(x2−6x+8)
Repeat the steps above for g(x)=x2−6x+8 .
The graph shows that 2 may be a zero.
Until a zero is discovered, use synthetic division to check the values.
2 is a zero.
Utilizing the output of the synthetic division, factor out a binomial.
Write a product of factors.
(−3 x+2)(x−2)(x−4)
Use the zero-product property.
0=(−3 x+2)(x−2)(x−4)−3 x+2=0x−2=0, x−4=0
Solve for x .
The real zeros of f are 23,2, and 4 .
Chapter 2 Solutions
Holt Mcdougal Larson Algebra 2: Student Edition 2012
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- 1. For the following subsets of R3, explain whether or not they are a subspace of R³. (a) (b) 1.1 0.65 U = span -3.4 0.23 0.4 -0.44 0 (})} a V {(2) | ER (c) Z= the points in the z-axisarrow_forwardSolve the following equation forx. leave answer in Simplified radical form. 5x²-4x-3=6arrow_forwardMATCHING LIST Question 6 Listen Use the given equations and their discriminants to match them to the type and number of solutions. 00 ed two irrational solutions a. x²+10x-2=-24 two rational solutions b. 8x²+11x-3=7 one rational solution c. 3x²+2x+7=2 two non-real solutions d. x²+12x+45 = 9 DELL FLOWER CHILD 10/20 All Changes S $681 22991arrow_forward
- 88 MULTIPLE CHOICE Question 7 Listen The following irrational expression is given in unsimplified form with four op- tions in simplified form. Select the correct simplified form. Select only one option. A 2±3√√2 B 4±√3 2±√ √3 D 1±√√3 DELL FLOWER CHILD 11/200 4 ± √48 4 ✓ All Changes Saved 165arrow_forwardUse the graph of y = f(x) to answer the following. 3- 2 -4 -2 -1 1 2 3 4 -1 2 m -3- + (d) Find all x for which f(x) = -2. If there is more than one value, separate them with commas or write your answer in interval notation, if necessary. Select "None", if applicable. Value(s) of x for which f(x)=-2: | (0,0) (0,0) (0,0) (0,0) 0,0... -00 None (h) Determine the range of f. The range is (0,0) Garrow_forwardWhat is g(f(4))arrow_forward
- 10) Multiply (8m + 3)² A) 8m²+11m+6 B) m² + 48m+9 C) 64m²+48m+9 D) 16m²+11m+6arrow_forwardLet R be field and X= R³/s Vector space over R M=(a,b,c)labic, e Rra+b= 3- <3 Show that Ms and why with proof. 1) is convexset and affine set of botost ii) is blanced set and symmetirs set of x iii) is hy per space and hyper plane ofx or hot iii) find f:MR st kerf = M 18/103 and finnd fiM→R/{0} st M= {xEX, f(t) = x, texiαER? jiii) show that Mis Maxsubspace or not and Mis a max. affine set or not.arrow_forwardFind The partial fraction decomposition for each The following 2× B) (x+3) a 3 6 X-3x+2x-6arrow_forward
- 1) Find the partial feraction decomposition for each of 5- X 2 2x+x-1 The following: 3 B) 3 X + 3xarrow_forwardT={(−7,1),(1,−1),(6,−8),(2,8)} Find the domain and range of the inverse. Express your answer as a set of numbers.arrow_forwardT={(−7,1),(1,−1),(6,−8),(2,8)}. Find the inverse. Express your answer as a set of ordered pairs.arrow_forward
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