Question

11. The polynomial f(x) = ** - 2x + 3x- ax + b when divided by (x-1)
and (x + 1) leaves the remainders 5 and 19 respectively. Find the values
of a and b. Hence, find the remainder when f(x) is divided by (x - 2).​

Answer 1

Step-by-step explanation:

Given The polynomial f(x) = x^4 - 2x^3 + 3x^2- ax + b when divided by    (x-1)  and (x + 1) leaves the remainders 5 and 19 respectively. Find the values  of a and b. Hence, find the remainder when f(x) is divided by        (x - 2).

• Given f(x) = x^4 – 2x^3 + 3x^2 – ax + b when divided by (x – 1) leaves remainder 5
• So f(1) = 1 – 2 + 3 – a + b = 5
• Or a – b = - 3 ------------1
• Also f(- 1) = 1 + 2 + 3 + a + b = 19
• Or a + b = 13 -----------2
• Now a – b = - 3
•   So  a + b = 13
• So we get 2a = 10
• Or a = 5
• Also a + b = 13
•      5 + b = 13
• Or b = 8
• Now x – 2 = 0 or x = 2
• So f(x) = x^4 – 2x^3 + 3x^2 – 5x + 8
• So f(2) = 2^4 – 2(2)^3 + 3(2)^2 – 10 + 8
•         = 16 – 26 + 12 – 2
•            = 10

Reference link will be

https://brainly.in/question/4580522