Multiple choice

In the Maths Olympiad of 2020 at Animal Planet, two representatives from the donkey's side, while solving a quadratic equation, committed the following mistakes: (i) One of them made a mistake in the constant term and got the roots as 5 and 9. (ii) Another one committed an error in the coefficient of x and he got the roots as 12 and 4. But in the meantime, they realized that they are wrong and they managed to get it right jointly. Which of the following could be the quadratic equation?

  1. x2 + 4x + 14 = 0

  2. 2x2 + 7x – 24 = 0

  3. x2 – 14x + 48 = 0

  4. 3x2 – 17x + 52 = 0
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

First person got roots 5 and 9 (sum 14, product 45). Mistake in constant term means sum is correct: x^2 - 14x + k = 0. Second person got roots 12 and 4 (sum 16, product 48). Mistake in x-coefficient means product is correct: x^2 - kx + 48 = 0. Combining these, the equation is x^2 - 14x + 48 = 0.

AI explanation

If one student made a mistake in the constant term, their calculated sum of the roots is correct, so the correct sum of the roots is 5 plus 9, which is 14. If the other student made a mistake in the coefficient of x, their calculated product of the roots is correct, so the correct product of the roots is 12 times 4, which is 48. For a monic quadratic equation x squared minus (sum)x plus product equals 0, substituting these values gives x squared minus 14x plus 48 equals 0.

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