Multiple choice

Directions: The following question consists of two quantities, Quantity I and Quantity II. You are to compare the two quantities and find the correct relationship between both the quantities. Quantity 1 Quantity 2 Sum of squares of roots of quadratic equation x2 – 2x – 3 = 0 12

  1. Quantity I > Quantity II

  2. Quantity I < Quantity II

  3. Quantity I ≥ Quantity II

  4. Quantity I ≤ Quantity II

  5. Quantity I = Quantity II, or No relation
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Roots of x^2 - 2x - 3 = 0 are (x-3)(x+1) = 0, so roots are 3 and -1. Sum of squares = 3^2 + (-1)^2 = 9 + 1 = 10. Quantity I = 10, Quantity II = 12. Thus, 10 < 12.

AI explanation

Using the factorization method, the roots of the equation x^2 - 2x - 3 = 0 are found by setting (x - 3)(x + 1) = 0, giving x = 3 and x = -1. The sum of the squares of these roots is 3^2 + (-1)^2, which equals 9 + 1 = 10. Comparing this to Quantity II, which is 12, we see that 10 is less than 12. Therefore, Quantity I < Quantity II.

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