Ganesh and Lokesh solved a quadratic equation. In solving it, Ganesh made a mistake in the constant term and got the roots as 6 and 7, while Lokesh made a mistake in the coefficient of x only and obtained the roots as 4 and 10. The correct roots of the equation are:
8, 5
Step 1:- Ganesh made mistake in constant term only,
Thus the sum of the roots was correct.
Step 2:- Sum of roots = 6 + 7 = 13 = −ba
Step 3:- Lokesh made mistake only in the coefficient of x. So the product of roots was correct.
Step 4:-
Thus product of roots = 10×4 = 40 = ca
Step 5:- Thus, the correct quadratic equation is x2–13x+40=0
⇒x2−8x−5x+40=0
⇒x(x−8)−5(x−8)=0
⇒(x−8)(x−5)=0
So, the roots are 8, 5.