## mukushla 2 years ago 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 : $$g(1)=-9$$

1. mukushla

i solved it with a painful method ... actually i've evaluated all of coefficients of g(x). but i lookin for a better method.

2. mukushla

@eliassaab @experimentX @satellite73

3. eliassaab

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.

4. experimentX

*