Multiple choice

In the Maths test two representatives, 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 got the roots as $12$ and $4$. But in the meantime, they realised that they are wrong and they managed to get right jointly. Find the correct quadratic equation.

  1. $x^2+4x+14=0$
  2. $2x^2+7x-24=0$
  3. $x^2-14x+48=0$
  4. $3x^2-17x+52=0$
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C Correct answer
Explanation

The first person got roots 5 and 9, so the sum is 14 and product is 45; since they erred in the constant, the coefficient of x (-14) is correct. The second person got roots 12 and 4, so the product is 48 and sum is 16; since they erred in the x-coefficient, the constant term (48) is correct. The correct equation is x^2 - 14x + 48 = 0.

AI explanation

The first student found the correct coefficient of x, so the correct sum of the roots is 5 + 9 = 14, making the correct b coefficient -14. The second student found the correct constant term, so the correct product of the roots is 12 * 4 = 48. Using the standard form x^2 - (sum)x + (product) = 0, the correct equation is x^2 - 14x + 48 = 0.

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