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Math Help - Probability of Distinct roots.

  1. #1
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    Probability of Distinct roots.

    k is uniformly chosen from the interval (-5,5) . Let p be the probability that the quartic f(x)=kx^4+(k^2+1)x^2+k has 4 distinct real roots such that one of the roots is less than -4 and the other three are greater than -1. Find the value of 1000p.
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  2. #2
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    Re: Probability of Distinct roots.

    let y=x2

    Your equation is ky^2+(k^2+1)y+k
    If you solve this equation for y the value of x will be \pm y^{1/2} So y is greater than or equal to zero if the roots are to be zero.

    If the roots are distinct
    y=0 is not a root and (k^2+1)^2-4 is not equal to zero

    Find the range of values of k so that one root is below -4 and the others are above -1 and express that range as a proportion of (-5,5) to get a probability.
    Last edited by Shakarri; March 19th 2013 at 04:39 AM.
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