Question

Ujakar and Keshab attempted to solve a quadratic equation.
- Ujakar made a mistake in writing down the constant term and got roots (4, 3).
- Keshab made a mistake in writing down the coefficient of $x$ and got roots (3, 2).
What will be the exact roots of the original quadratic equation?

• A. (6, 1)
• B. ($-3, -4$)
• C. (4, 3)
• D. ($-4, -3$)

Hint:

When two people make different mistakes, compare the correct parts of each to reconstruct the true equation.

Answer 1

The Correct Option is A

Let original quadratic be $x^2 + px + q = 0$.
From Ujakar’s roots (4, 3): sum $= 7 \Rightarrow p = -7$, product $= 12 \Rightarrow$ wrong constant $q' = 12$.
From Keshab’s roots (3, 2): sum $= 5 \Rightarrow p' = -5$ (wrong coefficient), product $= 6 \Rightarrow$ correct constant $q = 6$.
So actual: $x^2 - 7x + 6 = 0$, roots = 6 and 1.