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?

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?

anonymous · Answer

$$
(x-p_1)(x-p_2) = xx-p_1x-p_2x+(-p_1)(-p_2)=x^2-(p_1+p_2)x+p_1p_2
$$

anonymous · Answer

This means $$
p_1+p_2=63
$$And $$
p_1p_2=n
$$

anonymous · Answer

So, what two prime numbers add up to $63$?

anonymous · Answer

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

anonymous · Answer

Pick two that add up to $63$.