Polynomial Questions (1 Viewer)

[bos1234]

These are all the questions i asked on polynomials. Some are hard, some are easy. They are not in any order. I directed the answers to the threads I opened so you can see the full working posted by various BOS memebers. GOODLUCK!

Quadratics:Coroneos book
http://img156.imageshack.us/img156/5186/acw7.png

ANSWERS:

[URL="http://community.boredofstudies.org/13/mathematics-extension-1/131181/qn.html"]http://community.boredofstudies.org/13/mathematics-extension-1/131181/qn.html[/URL]

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When a polynomial is divided by (2x+1)(x-3) the remainder is 3x -1 . What is the remainder when the polynomial is divided by 2x+1

ANSWER:

[URL="http://community.boredofstudies.org/13/mathematics-extension-1/132376/ok-thanks.html"]http://community.boredofstudies.org/13/mathematics-extension-1/132376/ok-thanks.html[/URL]

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If one root of the eqn x^3 - bx^2 + cx - d = 0 is equal to the product of the other two, show that (c+d)^2 = d(b+1)^2

ANSWER:

 [URL="http://community.boredofstudies.org/13/mathematics-extension-1/132810/another-qn.html"]http://community.boredofstudies.org/13/mathematics-extension-1/132810/another-qn.html[/URL]

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Question and Answer:

[URL="http://community.boredofstudies.org/13/mathematics-extension-1/132539/answers-dont-match.html"]http://community.boredofstudies.org/13/mathematics-extension-1/132539/answers-dont-match.html[/URL]

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Write down the division identity when 30 divide 4 and 30 divide by 7

(b) Division of the polynomial P(x) by D9X) results in the quotient Q(x) and remainder R(x). Show that if P(x) is divided by Q(x), thew remainder will still b R(x). What is the quotient?

ANSWER:

[URL="http://community.boredofstudies.org/13/mathematics-extension-1/132329/2-polynomial-qns.html"]http://community.boredofstudies.org/13/mathematics-extension-1/132329/2-polynomial-qns.html[/URL]

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question and answer:

 [URL="http://community.boredofstudies.org/13/mathematics-extension-1/132665/quick-qn.html"]http://community.boredofstudies.org/13/mathematics-extension-1/132665/quick-qn.html[/URL]

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Show that the eqn of tghe normal to the curve x^2 = 4y at the pt (2t,t^2) is
x + ty -2 t - t^3 = 0

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4 unit question

the eqn
x^3 + 2x + 1 = 0 has roots a.b and c. FInd the equations with roots

a) a^2, B^2 and C^2

b) 1/a^2, 1/B^2 and 1/c^2

answer:

http://community.boredofstudies.org/14/mathematics-extension-2/132742/p-x-question.html

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Quadratics:CORONEOS

Show that the roots of one of the eqns
8ax^2(2x-1)+b^2=0, 4a^2x^2 +b^2(4x+1) = 0 must b unreal..

Show that the eqn (x+1)(x-4)=mx has 2 distinct roots for all real values of the constant m<!-- google_ad_section_end -->

answer:

[URL="http://community.boredofstudies.org/13/mathematics-extension-1/131652/help-2-questions.html"]http://community.boredofstudies.org/13/mathematics-extension-1/131652/help-2-questions.html[/URL]

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Given that P(x) = 2x^3 + x^2 -4x - 2 has a rational zero, find this zero and factorise P(x) over the set of real numbers.

Show the roots of the following equations are always real
(x-2p)(x-2q)=4r^2

answer:

[URL="http://community.boredofstudies.org/13/mathematics-extension-1/131494/polynomial-questions.html"]http://community.boredofstudies.org/13/mathematics-extension-1/131494/polynomial-questions.html[/URL]

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Well done u finished!
http://community.boredofstudies.org/13/mathematics-extension-1/132329/2-polynomial-qns.html

 

[fishy89sg]

sticky plz

 

[forevaunited]

I think i must be really bad at polynomials so here goes . .. Ok its from exercise 27.b) in the Fitzpatrick 3 unit book. Question 23.

Q: Given that (x-1) and (x+2) are two factors of 6x^4 + ax^3 - 17x^2 + bx - 4, find 'a' and 'b' and the other two factors

Ok so i can get a = -1 and b = 16 but then i am completely confused by the other part to the question. I would very much appreciate if someone could pinpoint my noobness

 

[bos1234]

Just multiply the factors and divide

P(x) = (x-1)(x+2).Q(x)

P(x)/(x-1)(x+2) = Q(x)

 

[forevaunited]

forgive me for being a bit slow here . . we were bascially told to go home and learn polynomials. . . so i have limited knowledge.

So multiplying the factors would give x^2 + x - 2.

So your saying divide 6x^4 - x^3 - 17x^2 +16x - 4 by x^2 + x - 2. I do not know how to do this.

 

[bos1234]

hold on ill do it neatly and post it here in about 5 minutes

EDIT: i dont know how to show you. The divide sing is not on the computer. But it should be in the book.

USE long division.

 

[pLuvia]

I think i must be really bad at polynomials so here goes . .. Ok its from exercise 27.b) in the Fitzpatrick 3 unit book. Question 23.

Q: Given that (x-1) and (x+2) are two factors of 6x^4 + ax^3 - 17x^2 + bx - 4, find 'a' and 'b' and the other two factors

Ok so i can get a = -1 and b = 16 but then i am completely confused by the other part to the question. I would very much appreciate if someone could pinpoint my noobness

If (x-1) and (x+2) are factors then x=1 and x=-2 are roots of the equation, sub those values in and you will form two equations and then simultaneously solve them to find a and b.

Then you can use long division to find the other factors

To bos1234: Doing your method won't find a and b, rather it is for the next bit after that

 

[forevaunited]

Thanks for the responses. Yeah i knew how to get a and b, bos was answering the second part of the question because that was the part i didn't know how to do.

So basically you divide 6x^4 - x^3 - 17x^2 +16x - 4 using long division by x^2 + x - 2. Ok well i havent learnt how to do that yet. We have only done simple ones involving only one x. eg. x-3 or x^2 + 3. Alritey thanks for that

 

[bos1234]

ok