Aman and Alok attempted to solve a quadratic equation. Aman made a mistake in writing down the constant term and ended up in roots (4, 3). Alok made a mistake in writing down the coefficient of x to gets roots (3, 2). The correct roots of the equation area)-4, -3b)6, 1c)4, 3d)-6, -1Correct answer is option 'B'. Can you explain this answer?

Question

Answer

Given Information:
- Aman made a mistake in writing down the constant term and ended up with roots (4, 3).
- Alok made a mistake in writing down the coefficient of x and ended up with roots (3, 2).
- The correct roots of the equation are (-4, -3).

Step 1: Understanding Quadratic Equations and its Roots
A quadratic equation is a polynomial equation of the second degree, which can be written in the form: ax^2 + bx + c = 0. The solutions of a quadratic equation are called its roots.

Step 2: Finding the Quadratic Equation
Let's assume the quadratic equation as ax^2 + bx + c = 0.

Step 3: Aman's Mistake
Aman made a mistake in writing down the constant term. Instead of c, he wrote a different constant term. This means the equation he wrote is: ax^2 + bx + d = 0.

Step 4: Alok's Mistake
Alok made a mistake in writing down the coefficient of x. Instead of b, he wrote a different coefficient of x. This means the equation he wrote is: ax^2 + cx + c = 0.

Step 5: Solving for Aman's Equation
Using the given roots (4, 3) for Aman's equation, we can substitute these values and get two equations:
(1) 16a + 4b + d = 0
(2) 9a + 3b + d = 0

Step 6: Solving for Alok's Equation
Using the given roots (3, 2) for Alok's equation, we can substitute these values and get two equations:
(3) 9a + 3c + c = 0
(4) 4a + 2c + c = 0

Step 7: Solving the System of Equations
Now, we can solve the system of equations (1)-(4) to find the values of a, b, c, and d.

Step 8: Equating the Correct Roots
After finding the values of a, b, c, and d, we can substitute them back into the original quadratic equation to check if the roots are correct.

Step 9: Conclusion
The correct roots of the quadratic equation are (-4, -3), which matches option B.

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