SOLUTION: Let α,β and λ be the roots of the equation 4x^3-19x^2+25x-7=0. Without solving the equation, find the values of a) α + β + λ b) αβ +&#9

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: Let α,β and λ be the roots of the equation 4x^3-19x^2+25x-7=0. Without solving the equation, find the values of a) α + β + λ b) αβ +&#9      Log On


   

Question 971249: Let α,β and λ be the roots of the equation 4x^3-19x^2+25x-7=0. Without solving the equation, find the values of
a) α + β + λ
b) αβ +αλ +βλ
c) αβλ
Thanks for help in advance.
Answer by anand429(138) About Me  (Show Source):
You can put this solution on YOUR website!
FOr roots a,b,c of the eqn.(say for alpha, beta and lambda)
4x%5E3-19x%5E2%2B25x-7=0
x%5E3-%2819%2F4%29x%5E2%2B%2825%2F4%29x-%287%2F4%29=0
Comparing with standard format of
x%5E3-%28a%2Bb%2Bc%29x%5E2%2B%28ab%2Bbc%2Bca%29x-%28abc%29=0
a%2Bb%2Bc+=+19%2F4
ab%2Bbc%2Bca+=+25%2F4 and
abc+=+7%2F4