JEE Exam > JEE Questions > If f(x) =an (x^n) +an-1( x^n-1) +... +a1(x) +...
Start Learning for Free
If f(x) =an (x^n) +an-1( x^n-1) +... +a1(x) +ao and if( a1-ao)+ (a3-a2)+..... =0 then one of the factor of f(x) is a) (x-1) b) (x +1) c) (x^2 +1) d) (x^2-1)? Any one solve this problem please?
Most Upvoted Answer
If f(x) =an (x^n) +an-1( x^n-1) +... +a1(x) +ao and if( a1-ao)+ (a3-a2...
Explanation:
The given function can be written as:
f(x) = anx^n + an-1x^n-1 + ... + a1x + ao
We need to find one of the factors of the given function f(x) based on the condition that:
(a1-ao) (a3-a2) ... = 0
Solution:
We know that (a1-ao) (a3-a2) ... = 0. This means that either one of the factors is equal to 0 or all the factors are equal to 0.
If one of the factors is equal to 0, then we can say that:
a1 - ao = 0 or a3 - a2 = 0 or ...
This means that there exists a value of x for which f(x) = 0. Therefore, (x - k) is a factor of f(x), where k is the value for which f(k) = 0.
Let us take an example to understand this:
If (a1 - ao) = 0, then we have:
f(x) = anx^n + an-1x^n-1 + ... + aox + ao
Since (a1 - ao) = 0, we have a1 = ao.
Therefore, we can write:
f(x) = ao(x^n-1 + x^n-2 + ... + x + 1)
Now, we know that x^n-1 + x^n-2 + ... + x + 1 is a factor of x^n+1.
Therefore, we can write:
f(x) = ao(x^n+1)/(x+1)
This means that (x+1) is a factor of f(x).
Similarly, we can prove that (x-1), (x^2+1), and (x^2-1) are also factors of f(x).
Therefore, the answer is (d) (x^2-1).
Attention JEE Students!
To make sure you are not studying endlessly, EduRev has designed JEE study material, with Structured Courses, Videos, & Test Series. Plus get personalized analysis, doubt solving and improvement plans to achieve a great score in JEE.
|
Explore Courses for JEE exam
|
|
Similar JEE Doubts
Top Courses for JEEView all
If f(x) =an (x^n) +an-1( x^n-1) +... +a1(x) +ao and if( a1-ao)+ (a3-a2)+..... =0 then one of the factor of f(x) is a) (x-1) b) (x +1) c) (x^2 +1) d) (x^2-1)? Any one solve this problem please?
Question Description
If f(x) =an (x^n) +an-1( x^n-1) +... +a1(x) +ao and if( a1-ao)+ (a3-a2)+..... =0 then one of the factor of f(x) is a) (x-1) b) (x +1) c) (x^2 +1) d) (x^2-1)? Any one solve this problem please? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about If f(x) =an (x^n) +an-1( x^n-1) +... +a1(x) +ao and if( a1-ao)+ (a3-a2)+..... =0 then one of the factor of f(x) is a) (x-1) b) (x +1) c) (x^2 +1) d) (x^2-1)? Any one solve this problem please? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If f(x) =an (x^n) +an-1( x^n-1) +... +a1(x) +ao and if( a1-ao)+ (a3-a2)+..... =0 then one of the factor of f(x) is a) (x-1) b) (x +1) c) (x^2 +1) d) (x^2-1)? Any one solve this problem please?.
If f(x) =an (x^n) +an-1( x^n-1) +... +a1(x) +ao and if( a1-ao)+ (a3-a2)+..... =0 then one of the factor of f(x) is a) (x-1) b) (x +1) c) (x^2 +1) d) (x^2-1)? Any one solve this problem please? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about If f(x) =an (x^n) +an-1( x^n-1) +... +a1(x) +ao and if( a1-ao)+ (a3-a2)+..... =0 then one of the factor of f(x) is a) (x-1) b) (x +1) c) (x^2 +1) d) (x^2-1)? Any one solve this problem please? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If f(x) =an (x^n) +an-1( x^n-1) +... +a1(x) +ao and if( a1-ao)+ (a3-a2)+..... =0 then one of the factor of f(x) is a) (x-1) b) (x +1) c) (x^2 +1) d) (x^2-1)? Any one solve this problem please?.
Solutions for If f(x) =an (x^n) +an-1( x^n-1) +... +a1(x) +ao and if( a1-ao)+ (a3-a2)+..... =0 then one of the factor of f(x) is a) (x-1) b) (x +1) c) (x^2 +1) d) (x^2-1)? Any one solve this problem please? in English & in Hindi are available as part of our courses for JEE.
Download more important topics, notes, lectures and mock test series for JEE Exam by signing up for free.
Here you can find the meaning of If f(x) =an (x^n) +an-1( x^n-1) +... +a1(x) +ao and if( a1-ao)+ (a3-a2)+..... =0 then one of the factor of f(x) is a) (x-1) b) (x +1) c) (x^2 +1) d) (x^2-1)? Any one solve this problem please? defined & explained in the simplest way possible. Besides giving the explanation of
If f(x) =an (x^n) +an-1( x^n-1) +... +a1(x) +ao and if( a1-ao)+ (a3-a2)+..... =0 then one of the factor of f(x) is a) (x-1) b) (x +1) c) (x^2 +1) d) (x^2-1)? Any one solve this problem please?, a detailed solution for If f(x) =an (x^n) +an-1( x^n-1) +... +a1(x) +ao and if( a1-ao)+ (a3-a2)+..... =0 then one of the factor of f(x) is a) (x-1) b) (x +1) c) (x^2 +1) d) (x^2-1)? Any one solve this problem please? has been provided alongside types of If f(x) =an (x^n) +an-1( x^n-1) +... +a1(x) +ao and if( a1-ao)+ (a3-a2)+..... =0 then one of the factor of f(x) is a) (x-1) b) (x +1) c) (x^2 +1) d) (x^2-1)? Any one solve this problem please? theory, EduRev gives you an
ample number of questions to practice If f(x) =an (x^n) +an-1( x^n-1) +... +a1(x) +ao and if( a1-ao)+ (a3-a2)+..... =0 then one of the factor of f(x) is a) (x-1) b) (x +1) c) (x^2 +1) d) (x^2-1)? Any one solve this problem please? tests, examples and also practice JEE tests.
|
|
Explore Courses for JEE exam
|
|
Suggested Free Tests
Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
|
© EduRev
|
Education Revolution
|
Follow Us
|
Signup to see your scores
go up within 7 days!
Access 1000+ FREE Docs, Videos and Tests
Takes less than 10 seconds to signup