Question

If x5 - 3x4 –ax3 + 3ax2 + 2ax + 4 is exactly divisible by (x – 2) then find the value of a.

Answer 1

Hello there
Since The given equation is exactly divisible by
x-2,it means that x-2 is the factor of the given equation and x=2 is one of the roots of the equation.
x5 - 3x4 –ax3 + 3ax2 + 2ax + 4
Putting x=2 in the above equation,it will become 0 since 2 is its root.
(2)^5-3(2)^4-a(2)^3+3a(2)^2+2a(2)+4=0
or,32-48-8a+12a+4a+4=0
or,8a-8=0
or,a=1
Hope it helps.

Answer 2

Answer:

x5 - 3x4 –ax3 + 3ax2 + 2ax + 4

Putting x=2.

(2)^5-3(2)^4-a(2)^3+3a(2)^2+2a(2)+4=0

32-48-8a+12a+4a+4=0

8a-8=0

a=1