SOLUTION: If (2x-1)(3x+2)=ax^2+bx+c for all values of x, find the smallest solution for y for the equation -cy^2+(a-1)y-(b+2)=0. Thanks for your help.

Algebra ->  Equations -> SOLUTION: If (2x-1)(3x+2)=ax^2+bx+c for all values of x, find the smallest solution for y for the equation -cy^2+(a-1)y-(b+2)=0. Thanks for your help.      Log On


   

Question 945633: If (2x-1)(3x+2)=ax^2+bx+c for all values of x, find the smallest solution for y for the equation -cy^2+(a-1)y-(b+2)=0. Thanks for your help.
Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!
If
%282x-1%29%283x%2B2%29=ax%5E2%2Bbx%2Bc for all values of x, then
%282x-1%29%283x%2B2%29=ax%5E2%2Bbx%2Bc
6x%5E2%2Bx-2=ax%5E2%2Bbx%2Bc+=> a=6, b=1, c=-2
the smallest solution for y for the equation -cy%5E2%2B%28a-1%29y-%28b%2B2%29=0 will be
-%28-2%29y%5E2%2B%286-1%29y-%281%2B2%29=0
2y%5E2%2B5y-3=0
2y%5E2-y%2B6y-3=0
%282y%5E2-y%29%2B%286y-3%29=0
2y%28y-1%29%2B3%282y-1%29=0
%28y%2B3%29+%282y-1%29+=+0
solutions:
if %28y%2B3%29+=+0 =>+y=-3
if +%282y-1%29+=+0 => 2y=1=>y=1%2F2
The smallest solution:+y=-3