prove that f(x)=x^2019 +x-1 has only one real root

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milcah answered 2 years ago

The Polynomial f(x) = X^3 - X^2 - X -1 has one real root a, which...

The Polynomial f(x) = X^3 - X^2 - X -1 has one real root a, which happens to be positive. This real number a satisfies the following properties: - for i = 1,2,3,4,5,6,7,8,9,10, one has {a^i} not equal to zero - one has [a] = 1, [a^2] = 3, [a^3] = 6, [a^4] = 11, [a^5] = 21, [a^6] = 7, [a^7] = 71, [a^8] = 130 (for a real number x, [x] denotes the floor of x and {x}...

Prove that: a) |sinx|<= |x| b) x = sin x has only one solution in real...

Prove that: a) |sinx|<= |x| b) x = sin x has only one solution in real number using mean value theorem

Suppose that x is real number. Prove that x+1/x =2 if and only if x=1. Prove...

Suppose that x is real number. Prove that x+1/x =2 if and only if x=1. Prove that there does not exist a smallest positive real number. Is the result still true if we replace ”real number” with ”integer”? Suppose that x is a real number. Use either proof by contrapositive or proof by contradiction to show that x3 + 5x = 0 implies that x = 0.

Prove that every polynomial having real coefficients and odd degree has a real root

Problem: Prove that every polynomial having real coefficients and odd degree has a real root This is a problem from a chapter 5.4 'applications of connectedness' in a book 'Principles of Topology(by Croom)' So you should prove by using the connectedness concept in Topology, maybe.

Determine the real root of f (x) = −25 + 82x − 90x2 + 44x3 −8x4...

Determine the real root of f (x) = −25 + 82x − 90x2 + 44x3 −8x4 + 0.7x5: Using python in bisection to determine the root to s = 10%. Employ initial guesses of xl = 0.5 and xu = 1.0; pls use python

Show that the equation has exactly one real root. 3x + cos(x) = 0

TOPOLOGY Let f : X → Y be a function. Prove that f is one-to-one and...

TOPOLOGY Let f : X → Y be a function. Prove that f is one-to-one and onto if and only if f[A^c] = (f[A])^c for every subset A of X. (prove both directions)

Prove: Every root field over F is the root field of some irreducible polynomial over F....

Prove: Every root field over F is the root field of some irreducible polynomial over F. (Hint: Use part 6 and Theorem 2.)

Consider the function f(x) = x - xcosx, which has a root at x = 0....

Consider the function f(x) = x - xcosx, which has a root at x = 0. Write a program to compare the rates of convergence of the bisection method (starting with a = -1, b = 1) and Newton’s method (starting with x = 1). Which method converges faster? Why?

Estimate a real root of the polynomial f(x) = 5x4-2x3-25x2-6x+45 between x=1 and x=2 (using bisection,...

Estimate a real root of the polynomial f(x) = 5x4-2x3-25x2-6x+45 between x=1 and x=2 (using bisection, Standard Newton-Raphson, Secant, and modified Newton-Raphson, and modified Secant methods). Show the detailed calculations for 5 iterations (for each method)

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