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. 5x2 - 32x + 51 = 0 II. y2 - 9 = 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
B Correct answer
Explanation

I: 5x^2 - 32x + 51 = 0. Roots: x = (32 +/- sqrt(1024 - 1020))/10 = (32 +/- 2)/10. x = 3.4 or 3. II: y^2 = 9, so y = 3 or -3. Comparing: x=3.4, y=3 (x>y); x=3.4, y=-3 (x>y); x=3, y=3 (x=y); x=3, y=-3 (x>y). Thus x >= y.

AI explanation

Using the factorization method for five x squared minus thirty two x plus fifty one equals zero, we find the roots are three and seventeen fifths. Solving y squared minus nine equals zero gives roots of three and negative three. Comparing these real values, the minimum x value of three is greater than or equal to the maximum y value of three, and seventeen fifths is also greater, so x is greater than or equal to y.

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