Tuesday, February 8, 2011

Prime numbers: Quadratic equation

Suppose the quadratic equation x²-48x+k has two posivtive solutions which are prime numbers. How many value of k are possible?



2 comments:

  1. 5 five
    215
    287
    407
    527
    551
    solution is easy: p1*p2=k and p1+p2=48
    just search in the 14 first primes less/equal 43

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  2. Yes, there are 5 distinct solutions.
    If m and n are the roots of the equation, we can write: (x - m)(x - n) = 0
    Or x^2 - (m + n)x + m*n = 0
    So, m + n = 48 <=> m = 48 - n
    We consider the primes as values for p and see if 48 - p is also prime. We end up with 5 solutions.

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