Show that there is a root of the equation below between 1 and 2. 4x36x2 +...
Fantastic news! We've Found the answer you've been seeking!
Question:
Transcribed Image Text:
Show that there is a root of the equation below between 1 and 2. 4x36x2 + 3x-2=0 SOLUTION Let f(x) = 4x² - 6x² + 3x - 2. We are looking for a solution of the given equation, that is, a number c between 1 and 2 such that f(c) = Therefore we take a = b = and N = in the Intermediate Value Theorem. We have f(1) =4-6 +3-2=-1 <0 f(2)= 32-24 +6-2=12>0 Thus f(1) < 0 <f(2); that is N = Ois a number between f(1) and f(2). Now f is continuous since it is a polynomial, so that the Intermediate Value Theorem says there is a number c between and such that f(c) = . In other words, the equation 4x³ -6x² + 3x- 2 = 0 has at least one root c in the interval ( In fact, we can locate a root more precisely by using the Intermediate Value Theorem again. Since f(1.2) =-0.128 <0 f(1.3) = 0.548 >0 a root must lie between f(1.22) =-0.007008 <0 f(1.23) = 0.056068 >0 So a root lies in the interval (1.22, 1.23). and .A calculation gives, by trial and error, Show that there is a root of the equation below between 1 and 2. 4x36x2 + 3x-2=0 SOLUTION Let f(x) = 4x² - 6x² + 3x - 2. We are looking for a solution of the given equation, that is, a number c between 1 and 2 such that f(c) = Therefore we take a = b = and N = in the Intermediate Value Theorem. We have f(1) =4-6 +3-2=-1 <0 f(2)= 32-24 +6-2=12>0 Thus f(1) < 0 <f(2); that is N = Ois a number between f(1) and f(2). Now f is continuous since it is a polynomial, so that the Intermediate Value Theorem says there is a number c between and such that f(c) = . In other words, the equation 4x³ -6x² + 3x- 2 = 0 has at least one root c in the interval ( In fact, we can locate a root more precisely by using the Intermediate Value Theorem again. Since f(1.2) =-0.128 <0 f(1.3) = 0.548 >0 a root must lie between f(1.22) =-0.007008 <0 f(1.23) = 0.056068 >0 So a root lies in the interval (1.22, 1.23). and .A calculation gives, by trial and error,
Expert Answer:
Answer rating: 100% (QA)
value of blank boxes are 0 f1 f2 fl 1 2 0 1 2 12 and 13 ... View the full answer
Related Book For
Posted Date:
Students also viewed these accounting questions
-
In Hermite interpolation we are looking for a polynomial p(x) (of degree 2n + 1 or less) such that p(x) and its derivative p'(x) have given values at n + 1 nodes. (More generally, p(x), p'(x), p"(x),...
-
In each case, show that u is a root of the quadratic equation, and find the other root. (a) x2 + ix - (4 - 2i) = 0; u = - 2 (b) x2 + 3(1 - i)x - 5i = 0; u = - 2 + i
-
Let f(x) = (x - 3)-2. Show that there is no value of in (1, 4) such that f(4) - f(1) = f'(c) (4 - 1). Why does this not contradict the Mean Value Theorem?
-
You have this information r*=2.5%, inflation premium =3%, default risk premium=3.5%, liquidity premium =2% and maturity risk premium =1.5%.What is the treasury bill rate?
-
Samstrun Electronics Store has three major departments: computers, televisions, and appliances. The appliance department has been a consistent money loser, as typified by the following recent monthly...
-
Gammaro Company uses standard costing. Tim Sweeney, the new president of Gammaro Company, is presented with the following data for 2017: Required 1. At what percentage of denominator level was the...
-
Helgeson Enterprises, Corp., completed the following selected transactions and prepared these adjusting entries during January: 2. Compute January net income or net loss under the accrual basis of...
-
In his book Capitalism and Freedom, economist Milton Friedman wrote on page 133: There is one and only one social responsibility of businessto use its resources and engage in activities designed to...
-
Simplify the following union and/or intersection. (-13, 9] U [5, c0)
-
Harper Morgan owns White Mountain Assessments in Laconia, New Hampshire. The standard workweek is 40 hours. For the weekly payroll ending September 9, 2022, checks dated September 14, 2022, complete...
-
Below are the accounts for Healthy Hospital on December 31, 2018 (note that all are shown as positive numbers but could be assets or liabilities and are not in any order). Given the following...
-
Crane Corporation's accounting records show the following at year-end December 31, 2022: Purchase Discounts Freight-In $7,450 Beginning Inventory $32,420 9,800 Ending Inventory 28,670 Freight-Out...
-
Barry Profit Corp.'s expected year-end dividend is $1.50, its required return is 12%, and their growth rate is 6%. What is Barry Profit's expected stock price in 8 years?
-
Finer Company uses a sales journal, purchases journal, cash receipts journal, cash payments journal, and general journal. Identify the journal in which each of the transactions should be recorded....
-
Compare two movies--such as Dangerous Minds and The Breakfast Club--that offer distinctly different portrayals of juvenile delinquency. Discuss their similarities and differences, and how they both...
-
Mercury Company has only one inventory pool. On December 31, 2024, Mercury adopted the dollar-value LIFO inventory method. The inventory on that date using the dollar-value LIFO method was $203,000....
-
Mbappe, Haaland and Bellingham are partners in a partnership called Golden Boys providing legal consulting services. The main day-to-day business operation is advising client on various legal issues....
-
What are some of the features of the Unified Process (UP)?
-
Find equations of the tangent line and normal line to the given curve at the specified point. y = 2xex, (0, 0)
-
If f(x) = x2 - 2x + 3, evaluate the difference quotient f (a + h) - f (a) / h
-
The demand function for a commodity is given by p = 2000 - 0.1x - 0.01x2 Find the consumer surplus when the sales level is 100.
-
In a survey of a simple random sample of students at a certain college, the sample mean time per week spent watching television was 18.3 hours and the margin of error for a 95% confidence interval...
-
Use the data in Exercise 4 to construct a 95% confidence interval for the mean IQ score. Exercise 4 An IQ test was given to a simple random sample of 75 students at a certain college. The sample mean...
-
The lifetime of a certain type of battery is known to be normally distributed with standard deviation = 20 hours. A sample of 50 batteries had a mean lifetime of 120.1 hours. It is desired to...
Study smarter with the SolutionInn App