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anonymous
 3 years ago
f(x)=2x^2−146x+c has 2 roots that are positive prime numbers. What is c?
anonymous
 3 years ago
f(x)=2x^2−146x+c has 2 roots that are positive prime numbers. What is c?

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anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0or 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
 3 years ago
Best ResponseYou've already chosen the best response.4use the sum of roots and product of roots formulae.

ParthKohli
 3 years ago
Best ResponseYou've already chosen the best response.4\[\dfrac{146}{2} = \alpha + \beta\]and\[\dfrac{c}{a} = \alpha \beta\]where \(\alpha\), \(\beta\) are the required prime roots.

ParthKohli
 3 years ago
Best ResponseYou've already chosen the best response.4Know any two prime numbers with sum \(73\)?

ParthKohli
 3 years ago
Best ResponseYou've already chosen the best response.4I meant\[\dfrac{(146)}{2} = \alpha + \beta\]

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0but 2 prime number tat makes 73??

ParthKohli
 3 years ago
Best ResponseYou've already chosen the best response.4Yeah, do you know any two such prime numbers with sum 73?

klimenkov
 3 years ago
Best ResponseYou've already chosen the best response.2If one of this primes is odd, the second must be even, because \(\alpha +\beta=73\). But how many even primes do you know?

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0Start from the very first prime number and work your way through. That's a hint for you.

ParthKohli
 3 years ago
Best ResponseYou've already chosen the best response.4There is only one even prime number.

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0I stress on the word "first" in that statement.

ParthKohli
 3 years ago
Best ResponseYou've already chosen the best response.4And of course, when you subtract the even prime, you will get another prime.

klimenkov
 3 years ago
Best ResponseYou've already chosen the best response.2@ParthKohli 17  prime. 2  even prime. If I subtract 17  2 = 15  I will get not prime.

ParthKohli
 3 years ago
Best ResponseYou've already chosen the best response.4No, in this case you must!

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0This case is NOT having such a situation though :)

ParthKohli
 3 years ago
Best ResponseYou've already chosen the best response.4This question would have no answer if you would not get another prime number after subtracting 2.

klimenkov
 3 years ago
Best ResponseYou've already chosen the best response.2Nobody guarantees you that this must have an answer.

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0Hey 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/
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