SOLUTION: Given that (x^2-ax+2)(x-b)=x^3-7x^2+14x+c, find the possible values of the constant a,b and c

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equation Customizable Word Problems -> SOLUTION: Given that (x^2-ax+2)(x-b)=x^3-7x^2+14x+c, find the possible values of the constant a,b and c      Log On


   

Question 346249: Given that (x^2-ax+2)(x-b)=x^3-7x^2+14x+c, find the possible values of the constant a,b and c
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
%28x%5E2-ax%2B2%29%28x-b%29=%28x%5E2-ax%2B2%29x-%28x%5E2-ax%2B2%29b
%28x%5E2-ax%2B2%29%28x-b%29=%28x%5E3-ax%5E2%2B2x%29-%28bx%5E2-abx%2B2b%29
%28x%5E2-ax%2B2%29%28x-b%29=x%5E3-ax%5E2-bx%5E2%2B2x%2Babx-2b
%28x%5E2-ax%2B2%29%28x-b%29=x%5E3-%28a%2Bb%29x%5E2%2B%282%2Bab%29x-2b
Comparing,
-%28a%2Bb%29=-7
1.a%2Bb=7
.
.
2%2Bab=14
ab=12
.
.
c=-2b
From eq. 1,
a=7-b
Substitute into eq. 2,
%287-b%29b=12
7b-b%5E2=12
b%5E2-7b%2B12=0
%28b-4%29%28b-3%29=0
Two solutions for b.
b-4=0
b=4
.
.
.
b-3=0
b=3
Now use the equation a=7-b and solve for the value of a for each value of b.
Then solve for c using c=-2b