Math Is Fun Forum

wanakev2

Member

Registered: 2009-06-25

Posts: 1

Help me complete my math assignment

Here the tricky questions:D

1(a) (POLYNOMIAL)
Determine the polynomial ƒ(x) satisfying the following conditions:

i)   Degree ƒ(x) is four
ii)  (x-1) is a factor of ƒ(x) and ƒ'(x)
iii)  ƒ(0)=3 and f'(0)=-5
iv)  when ƒ(x) is divided by (x-2), the remainder is 13

Hence, factorize ƒ(x) completely and solve the equation ƒ(x)=0.

Last edited by wanakev2 (2009-07-21 18:30:56)

wintersolstice

Real Member

Registered: 2009-06-06

Posts: 128

Re: Help me complete my math assignment

I don't have the full solution here, but I think I've deduced what the polynomomial is (I'm just not very good at factorising!)

Last edited by wintersolstice (2009-07-21 21:42:48)

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bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Help me complete my math assignment

Hi wintersolstice;

These are the factors:

or

Last edited by bobbym (2009-07-21 22:24:53)

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In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

juriguen

Member

Registered: 2009-07-05

Posts: 59

Re: Help me complete my math assignment

Hi!

I think the easiest way is to solve it backwards:

I hope I did the calculations OK!

Regarding the last question, you already know one answer, since (x - 1) is a factor, the solution is x = 1.

Use this website to expand f(x) and solve for other x:
http://www.quickmath.com

Jose

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“Make everything as simple as possible, but not simpler.” -- Albert Einstein

Ricky

Moderator

Registered: 2005-12-04

Posts: 3,791

Re: Help me complete my math assignment

You're giving all the information you need in order to factor the polynomial by algebraic methods alone.

(x-1) is a factor of ƒ(x) and ƒ'(x)

This means that (x-1) is a factor of multiplicity at least 2*.  Divide out by it twice using your favorite method of division and then you can easy quadratic equation the rest.

*Personally I don't remember this theorem from high school algebra, only graduate algebra when studying separable extensions.  Perhaps they teach it in high school?

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"In the real world, this would be a problem.  But in mathematics, we can just define a place where this problem doesn't exist.  So we'll go ahead and do that now..."