x^2-2ax+a^2 is a factor of 2x^3-5ax^2+8abx-36afind possible values of A and B when A does not equal 0

Question

x^2-2ax+a^2 is a factor of 2x^3-5ax^2+8abx-36a find possible values of A and B when A does not equal 0

Answer 1

Once we say,

 

x^2-2ax+a^2.  is a factor

 

Means,

 

(x-a)^2 is a factor

 

Means,  (x-a) is a factor

 

Substitute x= a in the expression given---

 

2a^3-5a^3+8a^2*b-36a

 

= 8a^2*b=36*a+3a^3

 

=8*a*b=36+3a^2

 

b= (3a^2+36)/8*a

 

All possible values of b are given by the above expression for various values of a

 

Since it it is given that a is not zero