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Math Help - Polynomial questions

  1. #1
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    Polynomial questions

    I tried doing these, but I always got the wrong answer or just got stuck on one part.

    1.Resolve algebraically
    x^3+4x^2-7x-10<0
    I have absolutely no clue on how to start with this one.
    2. 4+squareroot(x-2)=x
    I squared both sides, but it kept getting more and more complicated and really confused me.

    3.Determine the coordinates of the intersection points between the line y=x+7 and the circle (x+2)^2+(y-3)^2=52

    I tried substituting the line into the circle equation, but than I didn't know where to go from there.

    Thanks guys.
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  2. #2
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    Quote Originally Posted by Methodd View Post
    I tried doing these, but I always got the wrong answer or just got stuck on one part.

    1.Resolve algebraically
    x^3+4x^2-7x-10<0
    I have absolutely no clue on how to start with this one.
    Hint: factor x^3+4x^2-7x-10 = (x+1)(...)

    2. 4+squareroot(x-2)=x
    I squared both sides, but it kept getting more and more complicated and really confused me.
    Hint: rewrite 4+\sqrt{x-2}=x as \sqrt{x-2}=x - 4
    Now square both sides.

    3.Determine the coordinates of the intersection points between the line y=x+7 and the circle (x+2)^2+(y-3)^2=52

    I tried substituting the line into the circle equation, but than I didn't know where to go from there.
    Yes, your approach is correct. What did you get after substituting? Simplify, and you should have a quadratic equation.
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  3. #3
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    Yes, your approach is correct. What did you get after substituting? Simplify, and you should have a quadratic equation.
    I got x=-13+-\sqrt-900/20
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  4. #4
    Super Member Quacky's Avatar
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    Windsor, South-East England
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    Careful! I think you've made the mistake of square rooting both sides. You can't do that here because \sqrt{x^2+a^2} \neq x + a
    Let  x = 3 and a = 4 to prove this quite simply yourself.

    Anyway, going back to your question:
    y = x + 7
    Substituting that into (x+2)^2+(y-3)^2=52 gives:

    (x+2)^2+(x+7-3)^2=52
    (x+2)^2+(x+4)^2=52

    Do not square root here.
    You have to expand the brackets.
    x^2 + 4 x + 4 + x^2 + 8x + 16 = 52
    Tidy from here and factorize - you get a nice answer.
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  5. #5
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    Thanks guys, that really helped!
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