Question

uppose a is a simple root of the polynomial f(x) and g(x) is another polynomial of...

uppose a is a simple root of the polynomial f(x) and g(x) is another polynomial of degree > degree of f(x). Then g(x)/f(x) = (A/x-a) + other terms. Prove that A= g(a)/f'(a) by not using L'Habitial's rule.

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
Let p be an odd prime. Let f(x) ∈ Q(x) be an irreducible polynomial of degree...
Let p be an odd prime. Let f(x) ∈ Q(x) be an irreducible polynomial of degree p whose Galois group is the dihedral group D_2p of a regular p-gon. Prove that f (x) has either all real roots or precisely one real root.
write the polynomial equation f(x) in factored form with leading coefficient -2, and zeros -1(double root),...
write the polynomial equation f(x) in factored form with leading coefficient -2, and zeros -1(double root), 1 (single root), and 3 (single root). A) write f(x) in factored form B) What is its degree? C) what is its y-intercept D) sketch the graph showing the zeros and y-intercept
Let f(x) be a cubic polynomial of the form x^3 +ax^2 +bx+c with real coefficients. 1....
Let f(x) be a cubic polynomial of the form x^3 +ax^2 +bx+c with real coefficients. 1. Deduce that either f(x) factors in R[x] as the product of three degree-one polynomials, or f(x) factors in R[x] as the product of a degree-one polynomial and an irreducible degree-two polynomial. 2.Deduce that either f(x) has three real roots (counting multiplicities) or f(x) has one real root and two non-real (complex) roots that are complex conjugates of each other.
True or False, explain: 1. Any polynomial f in Q[x] with deg(f)=3 and no roots in...
True or False, explain: 1. Any polynomial f in Q[x] with deg(f)=3 and no roots in Q is irreducible. 2. Any polynomial f in Q[x] with deg(f)-4 and no roots in Q is irreducible. 3. Zx40 is isomorphic to Zx5 x Zx8 4. If G is a finite group and H<G, then [G:H] = |G||H| 5. If [G:H]=2, then H is normal in G. 6. If G is a finite group and G<S28, then there is a subgroup of G...
Prove any polynomial of an odd degree must have a real root.
Prove any polynomial of an odd degree must have a real root.
Consider the polynomial f(x) = x ^4 + x ^3 + x ^2 + x +...
Consider the polynomial f(x) = x ^4 + x ^3 + x ^2 + x + 1 with roots in GF(256). Let b be a root of f(x), i.e., f(b) = 0. The other roots are b^ 2 , b^4 , b^8 . e) Write b 4 as a combination of smaller powers of b. Prove that b 5 = 1. f) Given that b 5 = 1 and the factorization of 255, determine r such that b = α...
Let F be a field and let f(x) be an element of F[x] be an an...
Let F be a field and let f(x) be an element of F[x] be an an irreducible polynomial. Suppose K is an extension field containing F and that alpha is a root of f(x). Define a function f: F[x] ---> K by f:g(x) = g(alpha). Prove the ker(f) =<f(x)>.
1. This question is on the Taylor polynomial. (a) Find the Taylor Polynomial p3(x) for f(x)=...
1. This question is on the Taylor polynomial. (a) Find the Taylor Polynomial p3(x) for f(x)= e^ x sin(x) about the point a = 0. (b) Bound the error |f(x) − p3(x)| using the Taylor Remainder R3(x) on [−π/4, π/4]. (c) Let pn(x) be the Taylor Polynomial of degree n of f(x) = cos(x) about a = 0. How large should n be so that |f(x) − pn(x)| < 10^−5 for −π/4 ≤ x ≤ π/4 ?
1) find a cubic polynomial with only one root f(x)=ax^3+bx^2+cx +d such that it had a...
1) find a cubic polynomial with only one root f(x)=ax^3+bx^2+cx +d such that it had a two cycle using Newton’s method where N(0)=2 and N(2)=0 2) the function G(x)=x^2+k for k>0 must ha e a two cycle for Newton’s method (why)? Find the two cycle
Let f(x) be a polynomial and let r be a root of f(x). If x_1 is...
Let f(x) be a polynomial and let r be a root of f(x). If x_1 is sufficiently close to r then x_2 = i(x_1) is closer, x_3 = i(x_2) is closer still, etc. Here i(x) = x - f(x)/f'(x) is what we called the improvement function a. Let f(x)=x^2-10. Compute i(x) in simplified form (i.e. everything in one big fraction involving x). Let r = sqrt(10) and x_1=3. Show a hand computation of x_2 and then x_3, expressing both your...