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