Multiple choice

Directions: In the following question, two equations numbered I and II are given. You have to solve both the equations and mark the correct option. I. x2 + 6 + 7x = 0 II. y2 - 5y - 6 = 0

  1. x > y

  2. x ≥ y

  3. x < y

  4. x ≤ y

  5. x = y or relation between x and y cannot be established
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

I: x^2 + 7x + 6 = 0 => (x+6)(x+1) = 0 => x = -6, -1. II: y^2 - 5y - 6 = 0 => (y-6)(y+1) = 0 => y = 6, -1. Comparing values: x can be -6 or -1, y can be 6 or -1. In all cases, x <= y.

AI explanation

Factoring the first equation x^2 + 7x + 6 = 0 yields (x + 6)(x + 1) = 0, giving the roots x = -6 and x = -1. Factoring the second equation y^2 - 5y - 6 = 0 yields (y - 6)(y + 1) = 0, giving the roots y = 6 and y = -1. Since x = -1 is equal to y = -1 and x = -6 is less than both values of y, the overall relationship is x ≤ y.

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