The correct option is C b2+4aca2
Let the roots of the equation ax2−bx−c=0 be α,β.
Assuming that the roots are increased by k, so new roots are α+k,β+k.
By observation, we can see that difference of roots α−β remains same.
So, (α−β)2=(α+β)2−4αβ
=b2a2−4(−ca) =b2+4aca2