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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
A set S ⊂ Rn is a convex cone if it is a convex set, and for any x ∈ S and λ ≥ 0, λx ∈ S. Let S ⊂ Rn. Draw a few pictures to get used to coco(S)
The partners calculate that if they give the technician a raise of 8% and if they increase their own salaries by 5%, the gross annual salaries for all account personnel will rise from the current $1,086,000 to $1,156,500. What are the current annu..
One way is to try to find a function that best fits my data. I was thinking about one bestfit graph representing the correlation of all the ages of all the strikers and the goals they have scored.
Why can we use fixed point method to compute the solution of nonlinear equation y=g(x)? It's always convergence or not? If not, please gives a example to show it's divergence.
You are given the choice of three doors. Behind one is a new car and the others hide a barnyard animal for you to keep. After you choose door number one, your host (Monty) opens door three to reveal a goat
A computer sale is happening
Is there a strong evidence to indicate that the standard deviation of hole diameter exceeds 0.01 millimeters? Use? = 0.01. State any necessary assumptions about the underlying distribution of the data. Find the P-value for this test
assume that all of the cadburys dairy milk bars bought in england were the standard length of 11.4cm. when laid
You see a distant flash of lightning, and then you hear a thunderclap 2 s later. The sound of the thunder moves at 343 m/s.
what is the independent variable
What is the highest grade Tom can get if there is only one more 100 point test and all the tests are equally weighted. the teacher rounds final grades to the nearest integer.
Water is being pumped at a rate of 0.3 cubic meters per minute into a tank that has the shape of an inverted cone. The tank is 5 meters tall and has a diameter at the top of 2 meters. How fast is the water level rising when the depth of the water ..
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