Math, asked by deepaksassan01, 9 months ago

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).​

Answers

Answered by MisterIncredible
19

Answer :

Given :

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

(x-1) when divided leaves remainder 5

(x+1) when divided leaves remainder 19

Required to find :

  1. Values of " a " and " b "

Solution :

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

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