Multiple choice

Sachin and Rahul attempted to solve a quadratic equation. Sachin made a mistake in writing down the constant term and ended up in roots$(4,3)$. Rahul made a mistake in writing down a coefficient of $x$ to get roots(3,2). The correct roots of the equation are

  1. $-4, -3$
  2. $6, 1$
  3. $4, 3$
  4. $-6, -1$
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B Correct answer
Explanation

Since Sachin wrote the constant term incorrectly, his sum of roots (4 + 3 = 7) is correct, giving the coefficient of x as -7. Since Rahul wrote the coefficient of x incorrectly, his product of roots (3 * 2 = 6) is correct, giving the constant term as 6. The correct quadratic equation is x^2 - 7x + 6 = 0, which has roots 6 and 1.

AI explanation

Let the correct quadratic equation be x^2 - (sum)x + product = 0. Sachin found the correct sum of the roots as 7, since he only made a mistake in the constant term, but his product was 12. Rahul found the correct product of the roots as 6, since he only made a mistake in the coefficient of x, but his sum was 5. Combining the correct sum of 7 and the correct product of 6, the correct equation is x^2 - 7x + 6 = 0. Factoring this equation gives (x - 6)(x - 1) = 0, so the correct roots are 6 and 1.

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