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!!
implex bhai thodi hint de do...then will try again.
ReplyDeleteIts not difficult I know, par click nahi ho raha.
P.S. I revised equations. :)
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.
ReplyDeleteAm not able to factorize the roots of the second equation to come to a solution.
yaar a+b+c+d=0
ReplyDeleteso 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
damn!!!
ReplyDeletea+b+c+d=0
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.