If p(x)∈F[x] and deg p(x) = n, show that the splitting field for p(x)over F has degree at most n!.
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If p(x)∈F[x] and deg p(x) = n, show that the splitting field for p(x)
over F has degree at most n!.
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- Let p(z) and q(z) be analytic at z=z0, p(z0)≠0, and that q has a simple zero at z0. Show that:Show that the function u(x) = 3(1-2/|x|) is harmonic in Ω whenever Ω does not contain 0.1. If Rita receives $40.34 interest for a deposit earning 6% simple interest for 180 days, what is the amount of her deposit? (Round your answer to the nearest cent.) 2. Find the total amount that must be repaid on the following note described. $8,573 borrowed at 18.5% simple interest What is the total amount to be repaid 3 years, 125 days later? (Round your answer to the nearest cent.)
- 4) Let n- f(T) T" + > a; · T i=0 be a monic polynomial of degree n 21 with a; E Z for all 0 < iThe polynomial f= x^3- 4x + 2 is irreducible over Q. Let u be a root of f in some extension Q(u) of Q. Compute for (1 + 2u) (1 - u^2)Find z - transform F(z) of the function-1 f(nT) = d" T z + a -T | Z - O خيار 2 3 T z – a -T z + a |The Fourier transform of f(t) is F(w) = 2e bijw 9 + 3 Using the Convolution Theorem, find f(t) in the form f(t) = A H(t - to)et+D and enter the values of the constants A, to, C and D, as integers. Enter A: Enter to: Enter C Enter D:we have f: X→Y is a 1-1 function and Y is countable. Since f is 1-1, is it correct that this implies X ~ f(X) [which is f:X →f(X)] which further implies bijecton? Also, does this imply f(X) ⊆ Y?Compute the coefficient Fourier a, of the { T - r, 0Recommended textbooks for youAdvanced Engineering MathematicsAdvanced MathISBN:9780470458365Author:Erwin KreyszigPublisher:Wiley, John & Sons, IncorporatedNumerical Methods for EngineersAdvanced MathISBN:9780073397924Author:Steven C. Chapra Dr., Raymond P. CanalePublisher:McGraw-Hill EducationIntroductory Mathematics for Engineering Applicat…Advanced MathISBN:9781118141809Author:Nathan KlingbeilPublisher:WILEYMathematics For Machine TechnologyAdvanced MathISBN:9781337798310Author:Peterson, John.Publisher:Cengage Learning,Advanced Engineering MathematicsAdvanced MathISBN:9780470458365Author:Erwin KreyszigPublisher:Wiley, John & Sons, IncorporatedNumerical Methods for EngineersAdvanced MathISBN:9780073397924Author:Steven C. Chapra Dr., Raymond P. CanalePublisher:McGraw-Hill EducationIntroductory Mathematics for Engineering Applicat…Advanced MathISBN:9781118141809Author:Nathan KlingbeilPublisher:WILEYMathematics For Machine TechnologyAdvanced MathISBN:9781337798310Author:Peterson, John.Publisher:Cengage Learning,