Once you attempt the question then PrepInsta explanation will be displayed.
Infinite..
c=4 => x=1,4
c=-6 => x=-1,6
c=-14 => x=-2,7
c=-24 => x=-3,8
c=-36 => x=9,-4
c=-50 => x=-5,10
c=-55 => x=-6,11 and so on...
Additionally, For roots of the equation X^2-5X+C to be
rational integers we need to calculate its
DISCRIMINANT (Dis) which should be greater than or equal to 0.
i.e.
Dis=b^2-4ac
Dis>=0
here b=-5 , a=1 , c=C
hence Dis=(-5)^2 -4*1*C = 25-4C
therefore we can write the inequality as
25-4C>=0
or
25>=4C
there are infinite values of C ranging from -infinity to +6