The fourth degree polynomial equation x^4 - 7x^3 + 4x^2 + 7x - 4 = 0 has four real roots, a, b, c, and d. What is the value of the sum 1/(abc) + 1/(abd) + 1/(acd) + 1/(bcd)?
+2401 Try using vietas :))
simplfify 1/(abc) + 1/(abd) + 1/(acd) + 1/(bcd)
Then plug in the numbers from vietas equations
=^._.^=
+128407 Simplifying the sum....we have that.......
( abd)(acd)(bcd) + ( abc)(acd)(bcd) + ( abc)(abd)(bcd) + ( abc)(abd)(acd)
_______________________________________________________________ =
(abc) ( abc) ( acd) ( bcd)
(abcd)^2 ( a + b + c + d) (a + b + c + d)
_________________________ = ____________
(abcd)^3 abcd
By Vieta
(a + b + c + d) = - (-7) = 7
And
abcd = -4
So we have
7
__ = -7 / 4
-4
