Multiple choice

Directions: In the following question, two equations (I) and (II) are given. You have to solve both the equations and give answer. (I) 12x2 = -17x - 5 (II) 5y = y2 + 6

  1. x > y

  2. x < y

  3. x ≥ y

  4. x ≤ y

  5. x = y or no relation can be established between 'x' and 'y'
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

(I) 12x^2 + 17x + 5 = 0. Factors: 12x^2 + 12x + 5x + 5 = 0 -> 12x(x+1) + 5(x+1) = 0. Roots: x = -1, -5/12 (-0.41). (II) y^2 - 5y + 6 = 0. Factors: (y-2)(y-3) = 0. Roots: y = 2, 3. Comparing roots: -1 < 2, -1 < 3, -0.41 < 2, -0.41 < 3. Thus x < y.

AI explanation

Factoring the first equation 12x2 + 17x + 5 = 0 provides the roots x = -1/3 and x = -5/4. Factoring the second equation y2 - 5y + 6 = 0 provides the roots y = 2 and y = 3. Since both values of x are negative and both values of y are positive, x is always less than y.

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