Multiple choice

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

  1. (6, 1)

  2. (-3, -4)

  3. (4, 3)

  4. (-4, -3)
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A Correct answer
Explanation

Ujakar's roots (4, 3) imply the equation x^2 - 7x + C = 0. Keshab's roots (3, 2) imply the equation x^2 + Bx + 6 = 0. Combining these, the original equation is x^2 - 7x + 6 = 0. Factoring this gives (x - 6)(x - 1) = 0, so the roots are 6 and 1.

AI explanation

In a quadratic equation, the coefficient of x determines the sum of the roots and the constant term determines their product. Ujakar made a mistake in the constant term but copied the x coefficient correctly, so the correct sum of the roots is 4 + 3 = 7. Keshab made a mistake in the coefficient of x but copied the constant term correctly, so the correct product of the roots is 3 * 2 = 6. We need two numbers that add to 7 and multiply to 6, which are 6 and 1. The exact roots of the original equation are (6, 1).

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