## arun8408 Group Title f(x)=2x^2−146x+c has 2 roots that are positive prime numbers. What is c? one year ago one year ago

1. arun8408

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??

2. ParthKohli

use the sum of roots and product of roots formulae.

3. ParthKohli

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

4. ParthKohli

Know any two prime numbers with sum $$73$$?

5. ParthKohli

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

6. arun8408

ya its 73

7. arun8408

but 2 prime number tat makes 73??

8. ParthKohli

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

9. klimenkov

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

10. Azteck

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

11. ParthKohli

There is only one even prime number.

12. Azteck

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

13. ParthKohli

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

14. klimenkov

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

15. ParthKohli

No, in this case you must!

16. saloniiigupta95

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

17. ParthKohli

...?

18. ParthKohli

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

19. klimenkov

Nobody guarantees you that this must have an answer.

20. saloniiigupta95

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/

21. shubhamsrg

really? :O

22. saloniiigupta95

Yeah...

23. shubhamsrg

woah! :O

24. ParthKohli

LOL!!! ^^