If x3 - 6x2 + ax + b is divisible by (x2 - 3x + 2), then the values of a and b are:
Show answer & explanation
Correct answer: C
Explanation
The correct answer is Option 3 i.e a = 11 and b = -6.
| Understanding/Application |
|
x3 - 6x2 + ax + b is divisible by (x2 - 3x + 2) Let the quotient be x - p (x2 - 3x + 2) (x - p) = x3 - 6x2 + ax + b x3 - 3x2 + 2x - px2 + 3px - 2p = x3 - 6x2 + ax + b x3 - (3 + p)x2 + (2 + 3p)x - 2p = x3 - 6x2 + ax + b |
|
Comparing both sides - -(3 + p) = - 6 p = 3 2 + 3p = a a = 11 -2p = b b = -6 |