Given: Equation is x2−k2x+30kx−161x−64=0 Sum of roots =0 Concept Used: For quadratic equation ax2+bx+c=0 Sum of roots (α+β)=−b∕a Product of roots (α.β)=c∕a (α−β)2=(α+β)2−4α⋅β Calculation: We have x2−k2x+30kx−161x−64=0 ⇒x2−(k2−30k+161)x−64=0 α+β=(k2−30k+161)∕1=0 And α⋅β=−64∕1=−64 Now, We have to find α−β So, Using formula (α−β)2=(α+β)2−4α⋅β ⇒(α−β)2=(0)2−4×−64 ⇒(α−β)2=4×64 ⇒α−β=√(4×64) ⇒α−β=±16 ∴ The difference between the roots is 16 .