11by the definition of prime no. factors shud be one and itself
so any one factor should be 1
The no of positive integers x for which f(x)=x3-8x2+20x-13is a prime no is _______
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23 Answers
11
1ya pirate got it
only that no one mentioned the obvious thing i thought maybe i was missing somthing
33Yes i checked other factor too...
see for x-1=-1 ..
for x2-7x+13=±1 checked x-1 to be prime..
62yup philip you are right..
we have to do that too..
you have to check that the other is prime as well.. *I thought that was the more obvious part... sorry for not writing that down :(
1my doubt is not cleared bhaiyya even the method priyam used doesn't show what i wanted
1that is alright priyam but what i was asking was that even in this method we have to check whether the other factor comes out to b prime check out the eg i given above
62so priyam has solved this one :)
Philip I hope your doubt has been cleared too :)
33(x-1)=1
x=2
for x=2, x2-7x+13=3 prime.. for x=2
for (x-1)=-1
x=0
then x2-7x+13=13 but >0 so for x≠-1
-13 is not a prime naa[7]
for x2-7x+13=1 x=4,3
for x=4 (x-1)=3
for x=3 x-1=2
so for x=3,4 it is prime..
x2-7x+13=-1 no soln..
therefore for x=2,3,4 f(x) is prime..
11see the "or" in between
either factor should be 1 (-1 because other factor can be negative)
3we know by the definition of prime no
one of the factor shud be 1 or the no itself...
doubt is why the two factors shud be 1 or -1
341in such problems first check if it can be factored. Here (x-1) is a factor. can u take it from here?
1bhaiyya i have the same doubt as priyam above
do you mean we obtain values of x for which all except one factor is 1 and then check whether f(x) is prime
e.g. how do we do this (x-1)(x+2)=f(x)
3nishant sir can u help me why the condn is to be satisfied
x-1=1 or x-1 =-1
or x2-7x+13=1 or -1
62Arrey this is simple guys!!!
arrey so either x-1=1 or x-1 =-1
or x2-7x+13=1 or -1
13yeah... me too...
first of all... x3-8x2+20x-13 = (x-1)(x2-7x+13)
the other two factors are non-real rite...!!!
how to proceed further...?
1am not getting a hint of this question !!!!!!! [2]
we need to find x for which f(x)=prime... right ?
62x3-8x2+20x-13
well sankara...
the hint prophet gave is mro ethan sufficient.. you dont need to look anywhere else.. you dont need to goto trying and using graphs...
See u know one root as 1.. so u know the other roots... (if they are real)
Else u will have 2 terms as factors..
for being prime one has to be 1.... (infact all but 1 of these has to be 1 or -1) why?
3and then i dont know wat to do ..
Drawing a graph is the only way to solve the pbm