Multiple choice

In each of these questions, two equations (I) and (II) are given. You have to solve both the equations and give answer. I. 6x2 – 23√3x + 60 = 0 II. 2y2 + 3 √3y – 15 = 0

  1. if x > y

  2. if x ≤ y

  3. if x ≥ y

  4. if x < y

  5. if x = y or relationship between x and y can't be established
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Eq I: 6x^2 - 23sqrt(3)x + 60 = 0. Roots are (15sqrt(3)/6) and (8sqrt(3)/6) = 2.5sqrt(3) and 1.33sqrt(3). Eq II: 2y^2 + 3sqrt(3)y - 15 = 0. Roots are (-3sqrt(3) +/- sqrt(27 + 120))/4 = (-3sqrt(3) +/- 12.1)/4. x > y.

AI explanation

For equation I, splitting the middle term gives 6x^2 - 8*sqrt(3)x - 5*sqrt(3)x + 60 = 0, which factors to (2x*sqrt(5) - 5*sqrt(3))(3x*sqrt(5) - 4*sqrt(3)) = 0, wait let us use the correct factors (2x*sqrt(3) - 5)(3x*sqrt(3) - 4) = 0, giving x = 5*sqrt(3)/6 and 4*sqrt(3)/3. Using the quadratic formula for equation II yields y = (-3*sqrt(3) +/- 13*sqrt(3))/4, meaning y = sqrt(3) and -4*sqrt(3). Comparing these values, 5*sqrt(3)/6 > sqrt(3) and 4*sqrt(3)/3 > sqrt(3), while both are also greater than -4*sqrt(3), so x > y.

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