The difference between the roots of the equationx2 + ax +1=0 is less than 51/2 then set of all possible values ofa is?

let roots of equation areX and Y

then sum of roots=-a

product of roots XY=1

given difference of roots <5^1/2

squaring on both the sides

(X-Y)^2<5

(x-y)^2=(x+y)^2-4XY

=a^2-4<5

(a^2-9)<0

(a-3)(a+3)<0

a=(-3,3)