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 differenece of roots α−β remains same.
So,
(α−β)2=(α+β)2−4αβ =b2a2−4(−ca) =b2+4aca2