**Prime Roots**

*The x-intercepts of the equation y=x ^{2}-30x+k are prime numbers. What is/are the value(s) of K?*

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Correct answer were submitted by:

1. John Rey Jimenez. Negros Occidental High School

2. Arsh Singh. yourmathguru.com

3. Jomari Tan. DLSU

4. Ericson Diana. (school please)

5. Vincenzo Roque. University of the Philippines – Diliman

6. John Warner.English teacher.VHS. Bielefeld,Germany

7. Ceasar Ian Pedro. University of the Philippines-Diliman

8. Oen Can. Saint Mary’s University

9. Marlon Chris Malicsi, UST

10. Muthu Krishnan.Kle college , Bengaluru

11. Sebastian Pineda Berrío. Colombia.

12. Muthu Krishnan , Kle College , Bengaluru

Possible values for k are 23*7= 161, 19*11= 209 and 17*13= 221.

K = 161, 209 or 221

(UPD)

x^2 – 30x + k = y

at the x-intercepts y=0

30x – x^2 = k

x(30 – x) = k

x and (30 – x) are prime according to the problem

so x could be 7 gives (30-x)= 23 , 11 gives (30-x) = 19 , or 13 gives (30-x) = 17

=> k is either 7*23 = 161, 11*19 = 209 or 13*17 = 221

k = {161, 209, 221}

I am an English teacher at VHS Bielefeld in Germany.

Muthukrishnan , Kle college , bengaluru

values of k are 161,209,247

values of k are 161,209,221

The correct answer is 161,209,221, Please check the solution of Mr. Warner.