cricketfan10
New member
- Joined
- Jun 18, 2020
- Messages
- 3
I would look at the fact that given a quadratic:
[MATH]f(x)=ax^2+bx+c[/MATH]
which has the roots \(x_1\) and \(x_2\) that:
[MATH]x_1x_2=\frac{c}{a}[/MATH]
[MATH]x_1+x_2=-\frac{b}{a}[/MATH]
What do you get when you apply this to the given quadratic?
On second thought, let's observe that 1997 is a prime number, so given the roots are integers we can write:
[MATH]x^2+px+1997=(x+1)(x+1997)=0[/MATH]
or
[MATH]x^2+px+1997=(x-1)(x-1997)=0[/MATH]
What are the possible values for \(p\) and the roots associated with those values?