Question

find the value of a and b so that x^3-10x^2+ax+b^3 is exactly divisible by x-1 as well as x-2

Answer 1

Hey.

Here is the answer.

Polynomial , x³ +10x² + ax + b is exactly divisible by ( x -1) and (x -2)

it means x = 1 and 2 are the zeors of given polynomial .

so,
putting x = 1 in the expression , we get

(1)³ + 10(1)² +a(1) + b = 0

or, 1 + 10 + a + b = 0

or, a + b = -11 --------(1)

again putting x =2

(2)³ +10(2)² +a(2) + b =0

or, 8 + 40 + 2a + b = 0

or, 2a + b = -48 ----------(2)

solving equations (1) and (2)

a = -37 & b = 26


Thanks.