1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

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


    User Avatar
    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.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook