Multiple choice

Directions: In the following question, two equations numbered I and II are given in variables x and y. You have to solve both the equations and find out the relationship between x and y. Mark your answer accordingly. I. 3x2 + 18x + 15 = 0 II. 14y2 + 3y = 2

  1. x > y

  2. x < y

  3. x ≥ y

  4. x ≤ y

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

I: 3x^2 + 18x + 15 = 0 -> x^2 + 6x + 5 = 0 -> (x+5)(x+1) = 0. x = -5, -1. II: 14y^2 + 3y - 2 = 0 -> (7y-2)(2y+1) = 0. y = 2/7, -1/2. Comparing values: -5 < -1 < -0.5 < 0.28. Thus, x < y.

AI explanation

Factoring the first equation gives 3(x^2 + 6x + 5) = 0, which results in the roots x = -1 and x = -5. For the second equation, splitting the middle term gives 14y^2 + 7y - 4y - 2 = 0, yielding the roots y = -1/2 and y = 2/7. Since both values of x are negative and both values of y are positive, x is less than y.

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