Multiple choice

Directions: In each of these questions, two equations (I) and (II) are given. You have to solve both the equations and give answer. I. 20x2 – 108x + 144 = 0 II. 8y2 + 18y + 4 = 0

  1. x > y

  2. x ≤ y

  3. x ≥ y

  4. x < y

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

I: 20x^2 - 108x + 144 = 0 -> 5x^2 - 27x + 36 = 0. Roots are (27 +/- sqrt(729 - 720))/10 = (27 +/- 3)/10, so x = 3 or 2.4. II: 8y^2 + 18y + 4 = 0 -> 4y^2 + 9y + 2 = 0. Roots are (-9 +/- sqrt(81 - 32))/8 = (-9 +/- 7)/8, so y = -0.25 or -2. Comparing x and y, x > y.

AI explanation

Use the factorization method on equation I to split the middle term of 20x^2 - 108x + 144 = 0 into -60x and -48x, yielding (5x - 12)(4x - 12) = 0, so the roots of x are 12/5 and 3. For equation II, use the factorization method to split the middle term of 8y^2 + 18y + 4 = 0 into 16y and 2y, yielding (4y + 2)(2y + 2) = 0, which gives the roots y = -1/2 and y = -1. Because the smallest value of x is 2.4 and the largest value of y is -0.5, x > y.

Keep practicing — related questions