The number of integral values of a ; a (6,100) for which the equation [ x]^2+ x-a=0 has real roots; where [.] denotes greatest integer function is __________ .

Step-by-step solution

[ x ]^2+ x - a =0 [ x ]^2 and a are integral in nature x is integer. equation reduces to ^2 x + x - a =0 x ( x +1)= a a is product of consecutive integer Here a =12,20,30,42,56,72,90 a has 7 values.