## 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 Group Title

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 Group Title

use the sum of roots and product of roots formulae.

3. ParthKohli Group Title

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

4. ParthKohli Group Title

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

5. ParthKohli Group Title

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

6. arun8408 Group Title

ya its 73

7. arun8408 Group Title

but 2 prime number tat makes 73??

8. ParthKohli Group Title

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

9. klimenkov Group Title

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 Group Title

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

11. ParthKohli Group Title

There is only one even prime number.

12. Azteck Group Title

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

13. ParthKohli Group Title

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

14. klimenkov Group Title

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

15. ParthKohli Group Title

No, in this case you must!

16. saloniiigupta95 Group Title

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

17. ParthKohli Group Title

...?

18. ParthKohli Group Title

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

19. klimenkov Group Title

Nobody guarantees you that this must have an answer.

20. saloniiigupta95 Group Title

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 Group Title

really? :O

22. saloniiigupta95 Group Title

Yeah...

23. shubhamsrg Group Title

woah! :O

24. ParthKohli Group Title

LOL!!! ^^