Question

Let f(x) be polynomial function in field F[x]. f’(x) be the derivative of f(x). Given the...

Let f(x) be polynomial function in field F[x].
f’(x) be the derivative of f(x).
Given the greatest common factor (f(x), f’(x))=1.
And (x-a)|f(x). Show that (x-a)^2 can not divide f(x).

Homework Answers

Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
For each polynomial f(x) ∈ Z[x], let f ' (x) denote its derivative, which is also...
For each polynomial f(x) ∈ Z[x], let f ' (x) denote its derivative, which is also a polynomial in Z[x]. Let R be the following subset of Z[x]: R = {f(x) ∈ Z[x] | f ' (0) = 0}. (a) Prove that R is a subring of Z[x]. (b) Prove that R is not an ideal of Z[x].
Let f be a function for which the first derivative is f ' (x) = 2x...
Let f be a function for which the first derivative is f ' (x) = 2x 2 - 5 / x2 for x > 0, f(1) = 7 and f(5) = 11. Show work for all question. a). Show that f satisfies the hypotheses of the Mean Value Theorem on [1, 5] b)Find the value(s) of c on (1, 5) that satisfyies the conclusion of the Mean Value Theorem.
Let f(x) be a nonzero polynomial in F[x]. Show that f(x) is a unit in F[x]...
Let f(x) be a nonzero polynomial in F[x]. Show that f(x) is a unit in F[x] if and only if f(x) is a nonzero constant polynomial, that is, f(x) =c where 0F is not equal to c where c is a subset of F. Hence deduce that F[x] is not a field.
Given the polynomial function f (x) = (x + 3)(x + 2)(x −1) (a) Write all...
Given the polynomial function f (x) = (x + 3)(x + 2)(x −1) (a) Write all intercepts as ordered pairs (b) Find the degree of f to determine end behavior (c) Graph the function. Label all intercepts
Let f(x,y) be a function of x and y. The partial derivative of f(x,y) with respect...
Let f(x,y) be a function of x and y. The partial derivative of f(x,y) with respect to y is equivalent to the directional derivative of f(x,y) in the direction of the unit vector Select one: a. 〈0,1〉 b. 〈1,0〉 c. 〈1,1,1〉 d. 〈0,5〉
Let F be a field and let a(x), b(x) be polynomials in F[x]. Let S be...
Let F be a field and let a(x), b(x) be polynomials in F[x]. Let S be the set of all linear combinations of a(x) and b(x). Let d(x) be the monic polynomial of smallest degree in S. Prove that d(x) divides a(x).
1. Let f(x)=−x^2+13x+4 a.Find the derivative f '(x) b. Find f '(−3) 2. Let f(x)=2x^2−4x+7/5x^2+5x−9, evaluate...
1. Let f(x)=−x^2+13x+4 a.Find the derivative f '(x) b. Find f '(−3) 2. Let f(x)=2x^2−4x+7/5x^2+5x−9, evaluate f '(x) at x=3 rounded to 2 decimal places. f '(3)= 3. Let f(x)=(x^3+4x+2)(160−5x) find f ′(x). f '(x)= 4. Find the derivative of the function f(x)=√x−5/x^4 f '(x)= 5. Find the derivative of the function f(x)=2x−5/3x−3 f '(x)= 6. Find the derivative of the function g(x)=(x^4−5x^2+5x+4)(x^3−4x^2−1). You do not have to simplify your answer. g '(x)= 7. Let f(x)=(−x^2+x+3)^5 a. Find the derivative....
Determine the third Taylor polynomial of the given function at x = 0. f(x)=1/x+3
Determine the third Taylor polynomial of the given function at x = 0. f(x)=1/x+3
1 Approximation of functions by polynomials Let the function f(x) be given by the following: f(x)...
1 Approximation of functions by polynomials Let the function f(x) be given by the following: f(x) = 1/ 1 + x^2 Use polyfit to approximate f(x) by polynomials of degree k = 2, 4, and 6. Plot the approximating polynomials and f(x) on the same plot over an appropriate domain. Also, plot the approximation error for each case. Note that you also will need polyval to evaluate the approximating polynomial. Submit your code and both plots. Make sure each of...
given the polynomial function f(x)=x^2(x-3)(x+1) find x and y intercepts of f(x) and determine whether the...
given the polynomial function f(x)=x^2(x-3)(x+1) find x and y intercepts of f(x) and determine whether the graph of f crosses or touches the x-axis at each x-intercept.
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT