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We will now prove a fundamental result about polynomials: every non-zero polynomial of degreen (over a field F) has at most n roots. If you don't know what a field is, you can assume in thefollowing that F = R (the real numbers).
(a) Show that for any α ∈ F, there exists some polynomial Q(x) of degree n-1 and some b ∈ F such that P(x) = (x-α)Q(x) +b.
(b) Show that if α is a root of P(x), then P(x) = (x-α)Q(x).
(c) Prove that any polynomial of degree 1 has at most one root. This is your base case.(d) Now prove the inductive step: if every polynomial of degree n-1 has at most n-1 roots, thenany polynomial of degree n has at most n roots
Profits during the third quarter for a particular department store were $1,500,000. The pie chart below gives the results. Of the profits earned, how much were from jewelry sales?
Find the following values for the given function . (f-g)(3)= (fg)(3)=
A car is traveling at 90 km/h when the driver sees an accident 50 m ahead and slams on the brakes. What constant deceleration is required to stop the car in time to avoid a pileup? (Give your answer correct to two decimal places.)
Joshua, a merchant, promises in a signed writing to Pedro, a consumer, to hold an offer to sell goods open for five months. However, Joshua sells the goods to another consumer and Pedro sues him for breach of contract. Which of the following is tr..
151 g of water at 79.0°C are mixed with 75.2 g of water at 23.0°C. If no heat is lost to the surroundings, what is the final temperature of the water? The specific heat of water is 4.184 J/g·°C.
Show that x2 is a strictly convex function on R without using any knowledge of the differentiability of the function (that is, using the convex-combination condition of a convex function). Prove that a concave function is quasiconcave. Is the opposit..
A package can have a maximum combined length and girth of 108 inches. Find the dimensions of the package of maximum volume that can be sent. (assume that the cross section is a square)
Write the equation of the line in slope-intercept form, and graph using the slope and the y-intercept
What things can a researcher do to try to increase the magnitude of the d effect size? Suppose that you can increase the d effect size while holding group sizes n1 and n2 constant. How will an increase in d influence the magnitude of t ?
Give the open interval(s) where the function is decreasing. Give the open interval(s) where the function is concave down. Name the x-value where the absolute max occurs (if it exists).
Using excel I'm trying to create a probability tree showing all marginal, conditional and joint probabilities. Im also trying to develop a joint probability table and determine the probability that an employee selected at random would fail the man..
For a one sample confidence interval, the interval is calculated around the calculated sample mean (m).
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