Question

The quadratic equation x2 – 63x + n = 0 has two prime number roots. If you know that the equation has two prime roots, what value of “n” will make the statement true?

Answer 1

\[
(x-p_1)(x-p_2) = xx-p_1x-p_2x+(-p_1)(-p_2)=x^2-(p_1+p_2)x+p_1p_2
\]

Answer 2

This means \[
p_1+p_2=63
\]And \[
p_1p_2=n
\]

Answer 3

So, what two prime numbers add up to \(63\)?

Answer 4

Here are some prime numbers \[
2,\; 3,\; 5,\; 7,\; 11,\; 13,\; 17,\; 19,\; 23,\; 29,\; 31,\; 37,\; 41,\; 43,\; 47,\; 53,\; 59,\; 61
\]

Answer 5

Pick two that add up to \(63\).