Analysis of the Question:

- Mohan and Sohan are solving an equation.

- Mohan commits a mistake in the constant term and finds the roots 8 and 2.

- Sohan commits a mistake in the coefficient of x.

- We need to find the correct roots of the equation.


Understanding the Mistakes:

- Mohan's mistake is in the constant term, which means he made an error while calculating the value that does not involve x.

- Sohan's mistake is in the coefficient of x, which means he made an error while calculating the value that multiplies with x.


Finding the Correct Roots:

To find the correct roots of the equation, we need to consider the mistakes made by both Mohan and Sohan.


Mohan's Mistake:

- Let's assume the equation is in the form of ax^2 + bx + c = 0.

- Mohan's mistake is in the constant term, which means he incorrectly calculated the value of c.

- Mohan found the roots 8 and 2, which means the equation should satisfy the following conditions:

- When x = 8, the equation becomes a(8)^2 + b(8) + c = 0.

- When x = 2, the equation becomes a(2)^2 + b(2) + c = 0.

- Solving these two equations will give the correct value of c.

- Let's solve these equations to find the correct value of c:

- 64a + 8b + c = 0 ...(Equation 1)

- 4a + 2b + c = 0 ...(Equation 2)

- Subtracting Equation 2 from Equation 1, we get:

- 60a + 6b = 0 ...(Equation 3)

- Dividing Equation 3 by 6, we get:

- 10a + b = 0 ...(Equation 4)

- Now we have two equations (Equation 2 and Equation 4) with two variables (a and b).

- Solving these two equations will give the correct values of a and b.

- Once we have the correct values of a, b, and c, we can form the correct equation.

- Using the correct equation, we can find the correct roots.


Sohan's Mistake:

- Sohan's mistake is in the coefficient of x, which means he incorrectly calculated the value of b.

- Let's assume the correct values of a and c as obtained from Mohan's mistake.

- Sohan found the roots 8 and 2, which means the equation should satisfy the following conditions:

- When x = 8, the equation becomes a(8)^2 + b(8) + c = 0.

- When x = 2, the equation becomes a(2)^2 + b(2) + c = 0.

- Solving these two equations