The polynomial f(x)= x
4
– 2x3
+3x2
– 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 –3).
Answers
Take an online test Take Now
Login
Studyrankersonline
Ask a Question
When f(x) = x4 - 2x3 + 3x2 - ax is divided by x + 1 and x - 1 , we get remainders as 19 and 5 respectively .
0
votes
4.0k views
asked Dec 20, 2017 in Class IX Maths by ashu Premium (930 points)
When f(x) = x4 - 2x3 + 3x2 - ax is divided by x + 1 and x - 1 , we get remainders as 19 and 5 respectively .
Find the remainder if f(x) is divided by x - 3 .
Please log in or register to answer this question.
1 Answer
0
votes
answered Dec 20, 2017 by saurav24 Expert (1.4k points)
When f(x) is divided by (x+1) and (x-1) , the remainders are 19 and 5 respectively .
∴ f(-1) = 19 and f(1) = 5
⇒ (-1)4 - 2 (-1)3 + 3(-1)2 - a (-1) + b = 19
⇒ 1 +2 + 3 + a + b = 19
∴ a + b = 13 ------- (i)
Again , f(1) = 5
⇒ 14 - 2 × 13 + 3 × 12 - a × 1 b = 5
⇒ 1 - 2 + 3 - a + b = 5
∴ b - a = 3 ------ (ii)
solving eqn (i) and (ii) , we get
a = 5 and b = 8
Now substituting the values of a and b in f(x) , we get
∴ f(x) = x4 - 2x3 + 3x2 - 5x + 8
Now f(x) is divided by (x-3) so remainder will be f(3)
∴ f(x) = ∴ f(x) = x4 - 2x3 + 3x2 - 5x + 8
⇒ f(3) = 34 - 2 × 33 + 3 × 32 - 5 × 3 + 8
= 81 - 54 + 27 - 15 + 8 = 47
Answer:
This is your answer ☺️☺️
Step-by-step explanation:
please follow me
