Multiple choice

Ram and Sham solved a quadratic equation. In solving it, Ram made a mistake in the constant term only and got the roots as 8 and 2, while Sham made a mistake in the coefficient of x only and obtained - 9 and - 1 as roots. The correct roots of the equation are

  1. 8 and -1

  2. -9 and 2

  3. -8 and -2

  4. 9 and 1
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D Correct answer
Explanation

Ram's roots 8, 2 imply x^2 - 10x + 16 = 0. Since he missed the constant, the coefficient of x is -10. Sham's roots -9, -1 imply x^2 + 10x + 9 = 0. Since he missed the coefficient of x, the constant is 9. The correct equation is x^2 - 10x + 9 = 0. Roots are 9 and 1.

AI explanation

Let the correct quadratic equation be x^2 - Sx + P = 0, where S is the sum and P is the product of the correct roots. Ram made a mistake in the constant term P, but got the correct sum of roots S, so S = 8 + 2 = 10. Sham made a mistake in the coefficient of x S, but got the correct constant term P, so P = -9 * -1 = 9. The correct equation is x^2 - 10x + 9 = 0, and factoring this gives (x - 9)(x - 1) = 0, which means the correct roots are 9 and 1.

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