Multiple choice

Rahul and Simran attempted to solve a quadratic equation, which is in terms of x. However, Rahul misinterpreted the coefficient of x, resulting in the roots of -5 and +8. Simultaneously, Simran incorrectly read the constant term of the equation, leading to the roots of -3 and +9. Which of the following is/are the correct roots of the quadratic equation? I. 4 II. 10 III. -10 IV. -4

  1. Only I

  2. Only II

  3. Only I and III

  4. Only II and IV

  5. None of these
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Rahul misread the coefficient of x, so his constant term is correct. Roots -5 and 8 imply (x+5)(x-8) = x^2 - 3x - 40. Constant term is -40. Simran misread the constant, so her coefficient of x is correct. Roots -3 and 9 imply (x+3)(x-9) = x^2 - 6x - 27. Coefficient of x is -6. The equation is x^2 - 6x - 40 = 0. Roots are (x-10)(x+4) = 0, so 10 and -4.

AI explanation

Let the original equation be x^2 + bx + c = 0. Rahul misread the coefficient of x, so he used the correct constant term c, and the product of his roots equals c: (-5)(8) = -40. Simran misread the constant term, so she used the correct coefficient b, and the sum of her roots equals -b: (-3) + 9 = 6, meaning b = -6. The original equation is x^2 - 6x - 40 = 0, which factors to (x - 10)(x + 4) = 0. The correct roots are 10 and -4.

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