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mukushla
 2 years ago
let\[f(x)=x^4+2x^34x^2x+1\]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 : \(g(1)=9\)
mukushla
 2 years ago
let\[f(x)=x^4+2x^34x^2x+1\]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 : \(g(1)=9\)

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mukushla
 2 years ago
Best ResponseYou've already chosen the best response.0i solved it with a painful method ... actually i've evaluated all of coefficients of g(x). but i lookin for a better method.

mukushla
 2 years ago
Best ResponseYou've already chosen the best response.0@eliassaab @experimentX @satellite73

eliassaab
 2 years ago
Best ResponseYou've already chosen the best response.0You can find a, b ,c, d using a symbolic manipulator and you get \[ \begin{array}{c} a=3.14012 \\ b=0.571167 \\ c=0.437829 \\ d=1.27346 \end{array}\\ g(x)=x^6+4 x^53 x^413 x^33x^2+4 x+1\\ g(1)=9 \] This is probably the same way you did it. I will think about another method.
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