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Math Help - two quadratic equation problems

  1. #1
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    two quadratic equation problems

    1. Prove
    a^2 + b^2+c^2-ab-ac-bc > 0

    2. Let \alpha and \beta be the roots of the equation x^2 +kx +(p-k-1)=0 , where p and k are positive real numbers.
    (i) Find the quadratic equation whose roots are  \alpha -1 and \beta -1
    (ii) If p is prime and \alpha ,  \beta are integers, show that k = p - 1

    For question 2 I have trouble in (ii).

    Thanks in advance.
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  2. #2
    MHF Contributor
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    Quote Originally Posted by cakeboby View Post
    2. Let \alpha and \beta be the roots of the equation x^2 +kx +(p-k-1)=0 , where p and k are positive real numbers.
    (i) Find the quadratic equation whose roots are  \alpha -1 and \beta -1
    (ii) If p is prime and \alpha ,  \beta are integers, show that k = p - 1

    For question 2 I have trouble in (ii).

    Thanks in advance.
    Hi

    You should find in (i) x^2 + (k+2)x + p = 0

    If p is prime then \alpha-1=1 and \beta-1=p (or the other way)

    I let you finish
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