anonymous
  • anonymous
let\[f(x)=x^4+2x^3-4x^2-x+1\]the equation \(f(x)\) has 4 distinct real roots ; call them \(a,b,c,d\) suppose that \(g(x)\) is a degree 6 polynomial with roots \(ab,ac,ad,bc,bd,cd\). find the value of \(g(1)\). answer : \(g(1)=-9\)
Meta-math
jamiebookeater
  • jamiebookeater
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anonymous
  • anonymous
i solved it with a painful method ... actually i've evaluated all of coefficients of g(x). but i lookin for a better method.
anonymous
  • anonymous
@eliassaab @experimentX @satellite73
anonymous
  • anonymous
You can find a, b ,c, d using a symbolic manipulator and you get \[ \begin{array}{c} a=-3.14012 \\ b=-0.571167 \\ c=0.437829 \\ d=1.27346 \end{array}\\ g(x)=x^6+4 x^5-3 x^4-13 x^3-3x^2+4 x+1\\ g(1)=-9 \] This is probably the same way you did it. I will think about another method.

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experimentX
  • experimentX
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