Remember, it's Primes

Algebra Level 2

Let $\alpha$ and $\beta$ be roots of $x^2 - 63x + k$ . If $\alpha$ and $\beta$ are both prime numbers, what is $|\alpha - \beta|$ ?

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1 solution

Hua Zhi Vee
Jun 8, 2017

Using Vieta's formula, we know that $\alpha + \beta = 63$ . Since only even + odd = odd, we know that one of it is $2$ .

$2 + 61 = 63$

$|\alpha - \beta| = 59$