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 : $g(1)=-9$

Question

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 : $g(1)=-9$

anonymous · Answer

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 · Answer

@eliassaab  @experimentX  @satellite73

anonymous · Answer

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.

experimentx · Answer

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