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Problem Of The Week 15

with 4 comments

a, b, c, and d are the solutions of x^4+7x^2-3x+2=0. Find a polynomial with integer coefficients whose roots are (a+b+c)/d^2, (a+b+d)/c^2, (a+c+d)/b^2, and (b+c+d)/a^2. Find the sum of roots of this equation

A very simple problem, one should take about 1-1.5 mins to solve this. If you take more, revise equations please!!


Written by Implex

September 13, 2008 at 5:04 am

4 Responses

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  1. implex bhai thodi hint de do…then will try again.
    Its not difficult I know, par click nahi ho raha.
    P.S. I revised equations. 🙂


    September 15, 2008 at 11:30 am

  2. It has to do with the sums of roots, sum of product of roots taken 2 at a time, taken 3 at a time and product.
    Am not able to factorize the roots of the second equation to come to a solution.


    September 15, 2008 at 11:32 am

  3. yaar a+b+c+d=0
    so we need the equation with roots -1/a -1/b..
    so put x=1/x we will get the equation
    and find the sum of the roots of that equation we are done


    September 15, 2008 at 12:15 pm

  4. damn!!!
    so, the roots of the polynomial are -1/b,-1/c,-1/d,-1/a
    sum of roots=-3/2, prod=-1/2
    sum taken 2 at a time=-7/2
    taken 3 at a time=0
    so, the equation is 2X^4-3X^3-7X^2-1=0
    Hope there aren’t any calculation goof-ups.


    September 15, 2008 at 12:54 pm

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