Question

k is a prime number and f(x) = k has no solution

Answer 1

Answer:

Suppose x∈R is such that x+20x=p is a prime. Then x2−px+20=0 , and this equation has a solution x∈R if and only if p2–80≥0 . So the primes which admit no real solution are those that satisfy p<80−−√ , or 2 , 3 , 5 , and 7 . ■