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Homework Help: How do I calculate these questions relating to roots of quadratic equation?

  1. Jan 28, 2010 #1
    1. The problem statement, all variables and given/known data
    These two questions are very similar:
    1) Let c be a constant. If a and b are the roots of the equation x^2 + 2x - c = 0
    then 2b-a^2 = ?

    2) Let k be a constant. If a and b are the roots of the equation x^2 - 3x + k = 0
    Then a^2 + 3b = ?

    2. Relevant equations
    The answer to these 2 questions are -4-c and 9-k.

    3. The attempt at a solution
    For the first one, I was thinking about using the sum of roots and product of roots, I know that a+ b is -2 and ab must be c, but I don't know how to convert 2b-a^2 in to a new equation that only consists of a+b and ab . I used another approach, which is to turn the equation into 2 seperate ones by knowing the two roots given, a^2 + 2a - c = 0 and b^2 + 2b - c = 0. Then after some change of subject, I'll know that a^2 = c-2a and 2b = c-b^2 . But if I put in these two together, 2b-a^2 will equal to c-(b^2)-c+2a, which will finally give 2a-b^2, which doesn't really solve the problem....
    I thought of another way, which is to let those unknowns to be a random number. Since this is a multiple choice question, I can get the answer by try and error. However, I was thinking if there's a better way.
    Thanks :smile:
  2. jcsd
  3. Jan 28, 2010 #2


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    Science Advisor
    Homework Helper

    Your first approach was right. a+b=(-2). So b=(-2)-a. 2b-a^2=2(-2-a)-a^2=(-4)-(2a+a^2). Now finish up.
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