arun8408
f(x)=2x^2−146x+c has 2 roots that are positive prime numbers. What is c?
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arun8408
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or roots to be positive D>0 i.e. b^2 - 4ac >0
D=b^2 - 4ac = (-146)^2 - (4*2*c)>0
=>21316 - 8c>0
=>8c<21316
=> c<5329/2
is dis the ans??
ParthKohli
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use the sum of roots and product of roots formulae.
ParthKohli
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\[-\dfrac{146}{2} = \alpha + \beta\]and\[\dfrac{c}{a} = \alpha \beta\]where \(\alpha\), \(\beta\) are the required prime roots.
ParthKohli
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Know any two prime numbers with sum \(73\)?
ParthKohli
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I meant\[\dfrac{-(-146)}{2} = \alpha + \beta\]
arun8408
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ya its 73
arun8408
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but 2 prime number tat makes 73??
ParthKohli
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Yeah, do you know any two such prime numbers with sum 73?
klimenkov
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If one of this primes is odd, the second must be even, because \(\alpha +\beta=73\). But how many even primes do you know?
Azteck
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Start from the very first prime number and work your way through. That's a hint for you.
ParthKohli
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There is only one even prime number.
Azteck
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I stress on the word "first" in that statement.
ParthKohli
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And of course, when you subtract the even prime, you will get another prime.
klimenkov
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@ParthKohli
17 - prime. 2 - even prime. If I subtract 17 - 2 = 15 - I will get not prime.
ParthKohli
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No, in this case you must!
saloniiigupta95
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This case is NOT having such a situation though :-)
ParthKohli
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...?
ParthKohli
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This question would have no answer if you would not get another prime number after subtracting 2.
klimenkov
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Nobody guarantees you that this must have an answer.
saloniiigupta95
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Hey this is a problem of the present week's Brilliant Challenges... Shouldn't be discussed here actually...
Between, Awesome site for maths lovers...
https://brilliant.org/
shubhamsrg
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really? :O
saloniiigupta95
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Yeah...
shubhamsrg
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woah! :O
ParthKohli
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LOL!!! ^^