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Quadratic equation at x=0

  1. Nov 13, 2014 #1
    1. The problem statement, all variables and given/known data
    A functions is defined as f(x) = ax2 + bx + c, where a, b, c are real numbers. If f(3) = f(– 2) = 0, what is the value of f(0)?


    2. Relevant equations


    3. The attempt at a solution
    As function is 0 at 3, -2, therefore
    9a + 3b + c=0 also,
    4a -2 b + c=0
    c=-6a or c= 6b
    f(0)=c= 6a or -6b
    So the answer depends on the value of a or b (a= -b)

    However, the book states the following solution

    f(x) = ax2 + bx + c and f(3) = f(– 2) = 0 implies that 3 and (–2) are the roots of f(x).
    So, the quadratic equation is
    f(x) = (x – 3)(x + 2) = x2 – x – 6 = 0.
    Thus, f(0) = –6.

    However, if the roots are 3, -2 to a quadratic equ. , then required equation should be
    f(x) = k(x – 3)(x + 2)
    Am I right?





     
  2. jcsd
  3. Nov 13, 2014 #2

    pasmith

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    Yes. Unless the question tells you what [itex]a[/itex] is, there is no way to uniquely determine f(0) from the knowledge that f(3) = f(-2) = 0.
     
  4. Nov 13, 2014 #3

    Ray Vickson

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    You are right, but you should note that k = a; that is, f(x) = a(x-3)(x+2).
     
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