Multiple choice

Directions: In the following question, two equations (i) and (ii) are given. You have to solve both the equations and mark the correct option accordingly. (i) 4x2 + 13x - 12 = 0 (ii) 5y2 + 13y + 6 = 0

  1. x ≥ y

  2. x > y

  3. x = y, or no relation can be established between x and y.

  4. x ≤ y

  5. x < y
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Solve (i): 4x^2 + 13x - 12 = 0 -> (4x - 3)(x + 4) = 0 -> x = 3/4, -4. Solve (ii): 5y^2 + 13y + 6 = 0 -> (5y + 3)(y + 2) = 0 -> y = -3/5, -2. Comparing x and y: x can be 0.75 or -4, y can be -0.6 or -2. Since 0.75 > -0.6 and -4 < -2, no relation can be established.

AI explanation

Factoring equation (i), 4x^2 + 16x - 3x - 12 = 0, gives (4x - 3)(x + 4) = 0, so the roots for x are 3/4 and -4. Factoring equation (ii), 5y^2 + 10y + 3y + 6 = 0, gives (5y + 3)(y + 2) = 0, so the roots for y are -3/5 and -2. When x = 3/4, it is greater than both values of y, but when x = -4, it is less than both values of y. Because no single relation holds for all combinations, x = y or no relation can be established.

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