Two roots of the quadratic equation

*ax*^{2} +

*bx* +

*c* = 0 are given by,

From statement (A) alone,

∴

*p* and

*q* are not of the same sign.

[∵ If

*p* and

*q* are of same sign two digit number with same units digit, for example, 32 and 72, there difference will be a multiple of 10]

∴ Sum of

*p* and

*q* is a multiple of 10.

[For example, if

*p* = 32 and

*q* = −72,

*p* +

*q* = −40]

Therefore, we are not getting a unique solution from statement A alone.

From statement (B) alone,

[For example, if

*p* = 22 and

*q* = 12, units digit of (

*p* +

*q*)/2 will be 2, but if

*p* = 23 and

*q* = 13, units digit of (

*p* +

*q*)/2 will be 3, and so on]

Therefore, we are not able to find a unique solution from statement B alone.

From statement (A) and (B) together,

As we already know from statement A,

And, from statement B, we know,

Therefore, we are able to find a unique solution after combining both the statements A and B.

Hence, option 4.