Multiple choice

Directions: In the following question, two equations numbered I and II are given. You have to solve both the equations and choose the correct answer accordingly. I. 4A2 - 68A + 64 = 0 II. 8B2 + 40B + 32 = 0

  1. A < B

  2. A > B

  3. A = B, or No relation can be established between A and B.

  4. A ≤ B

  5. A ≥ B
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

I: 4A^2 - 68A + 64 = 0 simplifies to A^2 - 17A + 16 = 0, so (A-16)(A-1) = 0, A = 16 or 1. II: 8B^2 + 40B + 32 = 0 simplifies to B^2 + 5B + 4 = 0, so (B+4)(B+1) = 0, B = -4 or -1. Since all values of A are greater than all values of B, A > B.

AI explanation

Factoring equation one yields (4A - 4)(A - 16) = 0, so A is either 1 or 16. Factoring equation two yields 8(B + 1)(B + 4) = 0, so B is either -1 or -4. Since both values of A are greater than both values of B, the relationship is A > B.

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