Multiple choice

Directions: In the following question, two equations are given. You have to solve both the equations and choose the correct relationship accordingly. I. 7x2 + 17x - 12 = 0 II. 2y2 - 5y + 3 = 0

  1. x > y

  2. x ≥ y

  3. x < y

  4. x ≤ y

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

Solving 7x^2 + 17x - 12 = 0: (7x - 4)(x + 3) = 0, so x = 4/7 or -3. Solving 2y^2 - 5y + 3 = 0: (2y - 3)(y - 1) = 0, so y = 1.5 or 1. Comparing values, all possible x values are less than all possible y values.

AI explanation

Using the method of splitting the middle term for the first equation, we rewrite 7x^2 + 17x - 12 = 0 as 7x^2 + 21x - 4x - 12 = 0, which factors by grouping into (7x - 4)(x + 3) = 0, yielding x = 4/7 and x = -3. For the second equation, 2y^2 - 5y + 3 = 0 is rewritten as 2y^2 - 2y - 3y + 3 = 0, factoring into (2y - 3)(y - 1) = 0 and giving the roots y = 3/2 and y = 1. Comparing the highest values of both variables, 4/7 is approximately 0.57, which is less than 1, showing that every value of x is less than every value of y. Therefore, x < y.

Keep practicing — related questions