If two (positive) prime numbers are roots of the equation \(x^2-12x+k=0\), what is the value of k?

x^2 - 12x + k = 0

We are actually looking for two primes that sum to 12

7 and 5 seem to fit the bill

So

x^2 - 12x + 35 = 0 imply that

(x - 7) (x - 5) = 0

And 7 and 5 are the roots.....and k = 35