Multiple choice

Directions: In the following question, there are two quadratic equations. Study both the equations carefully and answer accordingly. I. 15x2 + 14x + 3 = 0 II. 15y2 - y - 2 = 0

  1. x > y

  2. x ≥ y

  3. x < y

  4. x ≤ y

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

I. 15x^2 + 14x + 3 = 0 -> (3x+1)(5x+3)=0 -> x = -1/3, -3/5 (-0.33, -0.6). II. 15y^2 - y - 2 = 0 -> (3y+1)(5y-2)=0 -> y = -1/3, 2/5 (-0.33, 0.4). Comparing: -0.33 <= -0.33, -0.33 < 0.4, -0.6 < -0.33, -0.6 < 0.4. Thus x <= y.

AI explanation

Factoring the first equation, fifteen x squared plus fourteen x plus three equals zero, gives five x plus one times three x plus three equals zero, which means the roots are negative one fifth and negative one. Factoring the second equation, fifteen y squared minus y minus two equals zero, gives five y minus two times three y plus one equals zero, which means the roots are two fifths and negative one third. Comparing these roots, negative one fifth is less than two fifths, and negative one is less than both two fifths and negative one third. Therefore, every value of x is less than or equal to every value of y, making x less than or equal to y the correct relation.

Keep practicing — related questions