Question

If f(x) = x2 - 63x + k is a quadratic polynomial such that both the zeroes are prime numbers, then the numbe of possible values of k is:

Answer 1

By Vieta’s formulas, the sum of the roots is 63.

Now all primes are odd except 2, but 63 is odd, so one root is even and one root is odd. So one of the roots is 2, and the other is 61, which is indeed prime.

Finally, k is the product of roots = 2 x 61 = 122.