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Math Help - quadratic trinomials

  1. #1
    rcs
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    quadratic trinomials

    pls help me solve for the roots of the quadratic trinomials
    quadratic trinomials-document-35-2-copy.jpg
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  2. #2
    Senior Member Educated's Avatar
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    This isn't a homework service. You have to show that you at least made an effort to try them rather than just getting other people to do it for you.

    We need proof that you actually tried, and then we can help you on parts that you get stuck on or cannot do.
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    HINT:
    ax^4 + bx^2 + c = 0
    Let k = x^2; then:
    ak^2 + bk + c = 0
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  4. #4
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    Those are NOT "quadratic trinomials" but they are of "quadratic type". That is, they can be changed to quadratic trinomials by a substitution like the one Wilmer used. Try it.
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  5. #5
    rcs
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    i can do for number 1 only

    x^4 - 11x^2 + 28 = 0
    (x^2 -7 ) ( x^2 -4 ) =
    (x^2 - 7 ) 0 | (x^2 - 4) = 0
    x^2 = 7 | x^2 = 4
    x = = + - sq. root of 7| x = +- of 2

    i dnt knw the rest beacuse i only knw the simple special products and factoring patterns.

    2. x^-4 - 13x^-2 + 36 = 0
    ( x^-2 + 6 )(x^-2 + 6 ) =
    i dnt knw next because it has a negative exponents and some of the rest of the given... sorry

    rotchkaroots lang.
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    Quote Originally Posted by rcs View Post
    2. x^-4 - 13x^-2 + 36 = 0
    Check that equation: I'm sure it should be x^-4 - 12x^-2 + 36 = 0

    Please use complete words; "dnt knw" are not words.
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  7. #7
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    Quote Originally Posted by rcs View Post
    i can do for number 1 only

    x^4 - 11x^2 + 28 = 0
    (x^2 -7 ) ( x^2 -4 ) =
    (x^2 - 7 ) 0 | (x^2 - 4) = 0
    x^2 = 7 | x^2 = 4
    x = = + - sq. root of 7| x = +- of 2

    i dnt knw the rest beacuse i only knw the simple special products and factoring patterns.

    2. x^-4 - 13x^-2 + 36 = 0
    ( x^-2 + 6 )(x^-2 + 6 ) =
    i dnt knw next because it has a negative exponents and some of the rest of the given... sorry

    rotchkaroots lang.
    Go back to x^-4- 13x^-2+ 36= 0.

    There are two ways to handle that:
    1) Let y= x^-2. Then x^-4= y^2 so the equation becomes y^2- 13y+ 36= 0. Once you have found y, x= 1/sqrt(y).

    2) Multiply the entire equation by x^4. You get 1- 13x^2+ 36x^4= 0 which becomes a quadratic by letting y= x^2: 36y^2- 13y+ 1= 0. Once you have found y, x= sqrt(y).
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  8. #8
    rcs
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    how is number 3 and 4 done sir... i tried to make the fraction with an exponent of 2... i really can hardly do it... how will i able to make the first term be with an exponent of 2 and make 1 for the second variable term.

    thnaks
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  9. #9
    MHF Contributor undefined's Avatar
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    Quote Originally Posted by rcs View Post
    how is number 3 and 4 done sir... i tried to make the fraction with an exponent of 2... i really can hardly do it... how will i able to make the first term be with an exponent of 2 and make 1 for the second variable term.

    thnaks
    \displaystyle x^{2/3}=\left(x^{1/3}\right)^2
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  10. #10
    rcs
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    i`m sorry if i have made u think that way (Educated) i just needed help. i never needed an insult sir/madam. i also tried my best to solve the problems in my own little way. I thank you so much for your help. it just happend that i wasn't able to show to you how i did it. Sorry.
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  11. #11
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    Quote Originally Posted by rcs View Post
    i`m sorry if i have made u think that way (Educated) i just needed help. i never needed an insult sir/madam. i also tried my best to solve the problems in my own little way. I thank you so much for your help. it just happend that i wasn't able to show to you how i did it. Sorry.
    "Educated" DID NOT insult you...he simply stated the rules that apply here.
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  12. #12
    rcs
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    pls check


    am i doing it right... pls check my work pls
    Last edited by rcs; September 16th 2010 at 02:32 AM.
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  13. #13
    rcs
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    pls check

    pls check my work
    Attached Thumbnails Attached Thumbnails quadratic trinomials-presentation1.jpg  
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  14. #14
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    You can check them yourself just by putting the numbers into the original equation. If x= -23/9, then x+ 3= -23/9+ 27/9= 4/9 and \sqrt{x+ 3}= 2/3.

    3(x+ 3)+ \sqrt{x+ 3}= 3(4/9) + 2/3= 4/3+ 2/3= 6/3= 2 so that is correct.

    If x= -2, then x+ 3= 1 and \sqrt{x+3}= 1.

    3(x+ 3)+ \sqrt{x+ 3}= 3(1)+ 1= 4, not 2, so that is not correct.

    The reason you got an incorrect answer was that, after getting M= 2/3 and -1 as the (correct) solutions to the quadratic, you set \sqrt{x+ 3}= -1 which is impossible- a square root is never negative.
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