Question

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

Answer 1

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??

Answer 2

use the sum of roots and product of roots formulae.

Answer 3

\[-\dfrac{146}{2} = \alpha + \beta\]and\[\dfrac{c}{a} = \alpha \beta\]where \(\alpha\), \(\beta\) are the required prime roots.

Answer 4

Know any two prime numbers with sum \(73\)?

Answer 5

I meant\[\dfrac{-(-146)}{2} = \alpha + \beta\]

Answer 6

ya its 73

Answer 7

but 2 prime number tat makes 73??

Answer 8

Yeah, do you know any two such prime numbers with sum 73?

Answer 9

If one of this primes is odd, the second must be even, because \(\alpha +\beta=73\). But how many even primes do you know?

Answer 10

Start from the very first prime number and work your way through. That's a hint for you.

Answer 11

There is only one even prime number.

Answer 12

I stress on the word "first" in that statement.

Answer 13

And of course, when you subtract the even prime, you will get another prime.

Answer 14

@ParthKohli
17 - prime. 2 - even prime. If I subtract 17 - 2 = 15 - I will get not prime.

Answer 15

No, in this case you must!

Answer 16

This case is NOT having such a situation though :-)

Answer 17

...?

Answer 18

This question would have no answer if you would not get another prime number after subtracting 2.

Answer 19

Nobody guarantees you that this must have an answer.

Answer 20

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/

Answer 21

really? :O

Answer 22

Yeah...

Answer 23

woah! :O

Answer 24

LOL!!! ^^