Question

find the value of a and b so that the polynomial x cube + 10 x square + a x + b is exactly divisible by x minus 1 and x + 2​

Answer 1

Answer:

a=7

b=-18

Step-by-step explanation:

Case 1:

dividend= x^3+10x^2+ax+b

divisor= x-1

quotient= x^2+11x+11+a

remainder= a+b+11=0. (equation 1)

Case 2:

dividend= x^3+10x^2+ax+b

divisor= x+2

quotient= x^2+8x-16+a

remainder= b-2a+32=0. (equation 2)

from equation 1,

a+b+11=0

b=-11-a. (equation 3)

from equation 2,

b-2a+32=0

b=-32+2a. (equation 4)

-11-a=-32+2a

2a+a=32-11

3a=21

a=21/3=7

substitute the value of a in

equation 3. (or) equation 4.

b=-11-a. b=-32+2a

b=-11-7. b=-32+(2×7)

b=-18. b=-18.

Answer 2

Answer:

answer will be - 18........