Question 160
Two friends, Marco and Ian, are talking about their ages.
Ian says, "My age is a zero of a polynomial with integer coefficients."
Having seen the polynomial $p(x)$ Ian was talking about, Marco exclaims, "You mean, you are seven years old? Oops, sorry I miscalculated! $p(7)=77$ and not zero."
"Yes, I am older than that," Ian's agreeing reply.
Then Marco mentioned a certain number, but realizes after a while that he was wrong again because the value of the polynomial at that number is 85.
Ian sighs, "I am even older than that number."
Determine Ian's age.
Ian says, "My age is a zero of a polynomial with integer coefficients."
Having seen the polynomial $p(x)$ Ian was talking about, Marco exclaims, "You mean, you are seven years old? Oops, sorry I miscalculated! $p(7)=77$ and not zero."
"Yes, I am older than that," Ian's agreeing reply.
Then Marco mentioned a certain number, but realizes after a while that he was wrong again because the value of the polynomial at that number is 85.
Ian sighs, "I am even older than that number."
Determine Ian's age.