Question

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

Answer 1

Answer:

a = b = 12

Step-by-step explanation:

Let's consider the given expression

f(x) = 2x + 3x - ax + b

(x-1) when divided leaves remainder 5

So, let

x - 1 = 0

x = 1

Hence,

f (1) = 2(1) + 3(1) - a(1) + b = 5

2 + 3 - a + b - 5 = 0

5 - a + b - 5 = 0

0 - a + b = 0

Then ,

b = a. -----------> equation 1

Similarly,

(x+1) when divided leaves remainder 19

So,

Let x + 1 = 0

x = - 1

Hence,

f(- 1) = 2(-1) + 3(-1) - a (-1) + b = 19

- 2 - 3 + a + b = 19

- 5 + a + b - 19 = 0 ( substitute the value of " b " from equation 1 )

- 5 + a + a - 19 = 0

- 24 + 2a = 0

2a = 24

a = 24/2

a = 12

hence ,

Value of a = 12

value of b = ?

but b = a ( from equation 1 )

So, b = 12

Therefore,

Value of a = 12

Value of b = 12

This states that ,

a = b = 12