Let (x) F[x], and let a F be a zero of f(x) of multiplicity v.

Question:

Let ƒ(x) ∈ F[x], and let a ∈ F̅ be a zero of f(x) of multiplicity v. Show that v > 1 if and only if α is also a
zero of f'(x).

Fantastic news! We've Found the answer you've been seeking!

Step by Step Answer:

Related Book For book-img-for-question

A First Course In Abstract Algebra

ISBN: 9780201763904

7th Edition

Authors: John Fraleigh

See More Books

Question Posted: Jan 16, 2023 02:50 AM

See More Questions

A zero of multiplicity m at p if and only if 0 = f ( p) = f'( p) = = f (m1)( p), but f (m)( p) 0.
Let V be an inner product space. Show that if v is orthogonal to w1, w2....wk, then v is orthogonal to every vector in span {w1, w2..... wk}.
Let f: X Y . Show that f displays increasing differences if and only if
With a global economy, the only way to achieve cost-effective control of greenhouse gases is to assure that every country imposes the same universal set of emissions standards. Discuss.
Electronic Repair Company repaired a high-definition television for Sarah Merrifield in December 2011. Sarah paid $80 at the time of the repair and agreed to pay Electronic Repair $80 each month for...
What are the criteria for the creation of a partnership?
Accounting with sales journal and purchases journal Non-GST version Tobys Traders Ltd uses sales and purchases journals in its accounting system. The following transactions occurred during April...
When interest rates decline, Patriot Bank has found that they get inundated with requests to refinance home mortgages. To better plan its staffing needs in the mortgage processing area of its...
Assume a hypothetical age that has not been assumed by other students. Assume you would like to invest in a zero-coupon bond in order to have $1000,000 in your retirement account when you get to the...
Show that if a finite extension E of a field F is a splitting field over F, then E is a splitting field of one polynomial in F[x].
Consider K = Q(2, 3). Referring to Exercise 17, compute each of the following (see Example 53.3). a. N k/Q (2) b. N K/Q (2 +3) c. N K/Q (6) d. N K/Q (2) e. Tr k/Q (2) f. Tr k/Q (2 + 3) g. Tr K/Q (6)...
MCO Leather Goods manufactures leather purses. Each purse requires 2 pounds of direct materials at a cost of $4 per pound and 0.8 direct labor hours at a rate of $16 per hour. Variable manufacturing...
The spherical harmonics satisfy the relation: V6,4) Yim (0,0) = -1(1+1) Ylm (0,4). Yim (0', p')Ym (0, q) can be written on (a) Show that IP-P Etzo Em 4m=-1 41 21+1+ = Eizo Em=-127 (0(-1) where 8(x))...
A 1 0 kg loggerhead sea turtle has a lung volume of 1 L and a body volume of 9 . 5 L ( lungs empty ) or 1 0 . 5 L ( lungs full ) . Assume a water density of 1 kg / L . The sea turtle fills its lungs...
A bungee cord exerts a nonlinear elastic force of magnitude F(x) = kx + k2x, where x is the distance the cord is stretched, k =204 N/m and k2 -0.223 N/m. How much work must be done on the cord to...
5. (1) The product given in the accompanying table are the most popular in the warehouse shown in the Figure below. How should these items be aligned along the main aisles? (10 marks) Product Receive...
Consider the function f: RR defined by f(x,y)=e+y-2r-3y. (a) Find and classify the critical points of f using the second derivative test. [4 marks] (b) Let P be the point (0,2). Using linear...
Successive plus and minus sights taken on a downhill line of levels are listed in Problems. The values represent the horizontal distances between the instrument and either the plus or minus sights....
Tanaka Company's cost and production data for two recent months included the following: March April Production (units).........300................600 Rent.....................$1,800............$1,800...
Refer to the previous exercise about the study of different HIV intervention programs. Suppose that the observed cell counts were actually twice as big as those reported in the original study. For...
Recall Exercise 8.1.12 about whether different generations view marriage differently. The corresponding data are available in the file MarriageViews. a. State the appropriate null and alternative...
In a study of the relationship between sleep apnea and hypertension (New England Journal of Medicine, 2000), researchers Peppard et al. categorized the participants by the severity of sleep apnea at...
corporate finance What the economic effect between 1MYR MYR to 0.21USD (write in paragraph and provide the link and citation) 14:37
deposit $80000, APY IS 1.25%, how much can I get after a year?
. You will retire 35 years from now. Once you reach retirement you plan on living 30 years (Anything longer and you will live off your children). You want to have enough money upon reaching...

Let (x) F[x], and let a F be a zero of f(x) of multiplicity v.

Question:

Step by Step Answer:

If x Fx and a F is a zero of x of multiplicity v it ...View the full answer

A First Course In Abstract Algebra

Students also viewed these Mathematics questions