JOMO 6, Short 6
Find the number of real solutions of x − 5 x 4 − 2 0 x 3 + 1 5 0 x 2 − 5 0 0 x + 6 2 5 = 0
The answer is 0.
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2 solutions
Concept here is -
D o m a i n o f g ( x ) f ( x ) = D o m a i n f ( x ) ∩ D o m a i n g ( x ) , g ( x ) = 0
excellent! :)
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Here its a removable discontinuity
I can write any linear function as the above say , x-1 , we can see it is continuous , it can be written as x − 1 ( x − 1 ) 2 , by doing this it can be proved that any linear function is discontinuous please help not able to understand
Can anybody explain please
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Looking at your example, x − 1 is identical to x − 1 ( x − 1 ) 2 for all real x except for x = 1 , since the second expression is undefined at x = 1 but the first is defined there. For the second expression we do have that
lim x → 1 x − 1 ( x − 1 ) 2 = 0 ,
but a function f ( x ) is only continuous at a value a such that
lim x → a f ( x ) = f ( a ) .
So x − 1 is continuous at x = 1 but x − 1 ( x − 1 ) 2 is not since it is undefined at this value. So they may seem identical, but in fact they are different functions. Hope that helps. :)
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@Brian Charlesworth – Yes sir understood we are treating x − 1 ( x − 1 ) 2 as a different function , the graph of it would also be a straight line but by definition of function it would be undefined at x =1 .
Thank you @brian charlesworth
I also did the same
I also did that.. I factored the numerator and got the value of x as 5 but then I realized that it will be such a mistake to take 5 as the solution because the answer goes indeterminate once we let x=5..
sir can you please explain that how you got to know that (x-5)^4 is the numerator of the expression
The problem poser gives a hint in the title ..2 was the answer of the Question with title jomo 7 short 2. 7-5=2..... In this question he has titled jomo6short6 is ans is 0. 6-6=0
Clearly the expression can be written as x − 5 x 4 − 2 0 x 3 + 1 5 0 x 2 − 5 0 0 x + 6 2 5 = x − 5 ( x − 5 ) 4 Now we have to be careful as it may seem that x = 5 is a solution however this is false. This is because the expression would then evaluate to 0 0 which is undefined. Therefore there are no real solutions and the answer is 0 .