Multiple choice

Directions: In the given question, two equations are given. You have to solve both the equations and mark the correct option. I. 5x2 - 19x + 12 = 0 II. 2y2 - 13y = -21

  1. x < y

  2. x ≤ y

  3. x > y

  4. x ≥ y

  5. x = y or the relationship cannot be established
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Eq I: 5x^2 - 19x + 12 = 0 -> (5x - 4)(x - 3) = 0 -> x = 0.8, 3. Eq II: 2y^2 - 13y + 21 = 0 -> (2y - 7)(y - 3) = 0 -> y = 3.5, 3. Comparing roots: x=0.8 < y=3.5, x=0.8 < y=3, x=3 < y=3.5, x=3 = y=3. Thus x <= y.

AI explanation

First, factor equation I, 5x2 - 19x + 12 = 0, to get (5x - 4)(x - 3) = 0, which gives the roots x = 4/5 and x = 3. Next, rewrite equation II as 2y2 - 13y + 21 = 0, which factors to (2y - 7)(y - 3) = 0, giving the roots y = 7/2 and y = 3. Since x is either 4/5 or 3, and y is either 3.5 or 3, every possible value of x is less than or equal to every possible value of y. Therefore, the relationship is x <= y.

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