if thepolynomial   2x3+ax2+3x-5  and  x3+x2-2x+a leave the same remainder when divided by (x-2) ,find the value of a.

Asked by deepa1973 | 13th Jun, 2015, 08:11: AM

Expert Answer:

By remainder theorem, the remainder when f(x)=2x3+ax2+3x-5 is divided by (x-2) is equal to f(2).
Similarly, the remainder when g(x)=x3+x2-2x+a is divided by (x-2) is equal to g(2).
Since, both the polynomial leave the same remainder, we get
f(2)=g(2)
=> 2X23 + aX22 + 3X2 - 5 = 2+ 2- 2X2 + a
=> 16+4a+6-5=8+4-4+a
=>4a+17=8+a
=> 3a=-9
=>a=-3

Answered by satyajit samal | 14th Jun, 2015, 08:44: AM