1 answer

In the polynomial #(x-1)(x-2)(x-3)cdots(x-100)#. Find the coefficient of #x^99# is?

Question:

In the polynomial #(x-1)(x-2)(x-3)cdots(x-100)#. Find the coefficient of #x^99# is?

Answers

#a_99 = 5050#

Explanation:

Calling #p_n(x) = prod_(k=1)^n(x-k)# we have

we now that their roots are #1,2,3,cdots,n#

and the coefficients for

#p_n(x) = a_0+a_1x+a_2x^2+ cdots + a_(n-1) x^(n-1) + x^n#

are liked to the roots values - For instance

#a_0 = n!, a_(n-1) = sum_(k=1)^n k = (n(n+1))/2#

so #a_99 = (100(100+1))/2 = 5050#

.

Similar Solved Questions

1 answer
Solve for Y(s), the Laplace transform of the solution y(t) to the initial value problem below....
Solve for Y(s), the Laplace transform of the solution y(t) to the initial value problem below. y"' + 8y = 42 - 3, y(0) = 0, y'(0) = -5 Click here to view the table of Laplace transforms. Click here to view the table of properties of Laplace transforms. Y(s) =...
1 answer
8. LO 13.3 Explain the role and purpose of the Global Reporting Initiative. 9. LO 13.3...
8. LO 13.3 Explain the role and purpose of the Global Reporting Initiative. 9. LO 13.3 Explain the role and purpose of the Sustainability Accounting Standards Board. 10. LO 13.3 Explain the role and purpose of the Integrated Reporting Framework....
1 answer
Let X be an exponential random variable with mean μ=2.0. Define the event A to be...
Let X be an exponential random variable with mean μ=2.0. Define the event A to be FXM(x/Ac) conditional probability distribution function fx /バ(x/ Ac ) , function and conditional density where A denotes the complement of the event A. [15 points] X/A...
1 answer
Run-length encoding (RLE) is a simple "compression algorithm" (an algorithm which takes a block of data...
Run-length encoding (RLE) is a simple "compression algorithm" (an algorithm which takes a block of data and reduces its size, producing a block that contains the same information in less space). It works by replacing repetitive sequences of identical data items with short "tokens" th...
1 answer
Measures of liquidity, Solvency, and Profitability The comparative financial statements of Marshall Inc. are as follows....
Measures of liquidity, Solvency, and Profitability The comparative financial statements of Marshall Inc. are as follows. The market price of Marshall common stock was $ 59 on December 31, 20Y2 Determine the following measures for 20Y2, rounding to one decimal place, except for dollar amounts, which ...
1 answer
How fast must an electron move so that its total energy is 17% more than its...
How fast must an electron move so that its total energy is 17% more than its rest mass energy? Give your answer as a fraction of c. Express your answer using three significant figures....
1 answer
Please help with both a and b 5. a) Let f(x, y, 2) = (x +y...
please help with both a and b 5. a) Let f(x, y, 2) = (x +y = 42²) Let & be the region between the spheres xaty 2+ 2 =4. and X² +4² +22 9 with 220 compole JE S S f (x, y, z) dv but do not evaluate the intergral to hind the volume on the 3D region bounded by planes -X=0,4 = x + x+y=...
1 answer
29. The effects of acetylcholine can be either excitatory or inhibitory. The effect depends on A....
29. The effects of acetylcholine can be either excitatory or inhibitory. The effect depends on A. the type of calcium channels in the presynaptic neuron B. the type of acetylcholine-activated channel in the post-synaptic membrane C. the presence or absence of acetylcholinesterase in the synaptic cle...
1 answer
6. (6 points) Briefly answer the following pts) The two concepts of Mechanism and Policy are central to the implementation of protection. Briefly describe each of these concepts. Identify the role,...
6. (6 points) Briefly answer the following pts) The two concepts of Mechanism and Policy are central to the implementation of protection. Briefly describe each of these concepts. Identify the role, if any, of the operating a. (4 system and user in each concept. b. (8 pts) Briefly define a Stack Buff...
1 answer
Casinos and Crime Earl Grinols and David Mustard are economists and, like a lot of people,...
Casinos and Crime Earl Grinols and David Mustard are economists and, like a lot of people, intrigued by both casinos and crime. In their case, they were especially curious about whether the first causes the second. It does, according to their study. Eight percent of crime occurring in counties that ...
1 answer
Calculate the pole and zero for R = 1kOhm and C = 10uF. Draw magnitude and...
Calculate the pole and zero for R = 1kOhm and C = 10uF. Draw magnitude and phase plots as a function of frequency. R + + CE Yout(t) (a) R + + Vin(s) = Vour(s) SC (b) FIGURE 14.27 (a) A simple resistor-capacitor circuit, with an input voltage and output voltage specified. (b) The s-domain equiva...
1 answer
If f(x) In(x) find f '(1). ,10 x f'(1) = 2 x Enhanced Feedback Please try...
If f(x) In(x) find f '(1). ,10 x f'(1) = 2 x Enhanced Feedback Please try again using the Quoti Need Help? Read It Submit Answer Look up the formulas below in your text and fill in the rest of the formula. You need to memorize these formulas. (In x)= х (log, *)= d dx(In(x)In(b))...
1 answer
John ties a 15-m-long, 5 kg rope to a wall and stretches it out horizontally, placing...
John ties a 15-m-long, 5 kg rope to a wall and stretches it out horizontally, placing it under a tension of 2000 N, which gives the rope a wave speed of 77.5 m/s. He then creates a wave in the rope by oscillating one end. a) What is the frequency of the third harmonic for this rope? b) What is the f...
1 answer
If fire get burn in presence of air so how sun burn?
If fire get burn in presence of air so how sun burn?...
1 answer
Question 2 Londen Industries Limited as the following information 2012 July August 16,000 September 18.000 18,800...
Question 2 Londen Industries Limited as the following information 2012 July August 16,000 September 18.000 18,800 October 22,000 23,600 November 30,000 25,600 Each unit requires 6 pounds of raw materials that are eximated to cost an average of 110 pound. They also have a policy of ma each month equa...
1 answer
Luzadis Company makes furniture using the latest automated technology. The company uses a job-order costing system...
Luzadis Company makes furniture using the latest automated technology. The company uses a job-order costing system and applies manufacturing overhead cost to products on the basis of machine-hours. The predetermined overhead rate was based on a cost formula that estimates $520,000 of total manufactu...
1 answer
Identical cellos are being tested. One is producing a fundamental frequency of 248 Hz on a...
Identical cellos are being tested. One is producing a fundamental frequency of 248 Hz on a string that is 1.06 m long and has a mass of 100.0 g. On the second cello the same string is fingered to reduce the length that can vibrate. If the beat frequency produced by these two strings is 4.0 Hz, what ...
1 answer
Styles First we will learn how to evaluate binomial distribution with the help of Excel. Let's...
Styles First we will learn how to evaluate binomial distribution with the help of Excel. Let's flip a coin n times and count how many tails we are going to get. If n=0, then no coin is tossed and the only option is 0 tails. Therefore P(0)=1, the mean is 0 and the standard deviation is 0. We are ...
1 answer
I have resubmitted this with images that I hope are clearer. Thank you. Solar Entertainment is...
I have resubmitted this with images that I hope are clearer. Thank you. Solar Entertainment is a provider of cable, Internet, and on-demand video services. Solar currently sends monthly bills to its customers via the postal service. Because of a concern for the environment and recent increases in po...
1 answer
(2) Calculate the following integrals: х 2.x3 – 4x + 3 -dx (x + 1)2(x2 +1)...
(2) Calculate the following integrals: х 2.x3 – 4x + 3 -dx (x + 1)2(x2 +1) Java 2 - 25 2 dx x4V x2 – 25 (3) Explain why, using the techniques we've learned so far, we are able to calculate the integral of any rational function. (A rational function is one of the form p(x) where...