Multiple choice

Directions: In the given question, two equations are given. You have to solve both the equations and mark the correct option. (i) 3A2 - 15A = 14A - 35 - 3A2 (ii) 10B2 - 65B = 96B - 624

  1. A < B

  2. A > B

  3. A ≥ B

  4. A ≤ B

  5. The relationship between A and B cannot be established.
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Solving the first quadratic equation 6A^2 - 29A + 35 = 0 gives the roots A = 2.5 and A = 2.33. Solving the second quadratic equation 10B^2 - 161B + 624 = 0 gives the roots B = 9.6 and B = 6.5. Since both values of A are strictly less than both values of B, we establish that A < B.

AI explanation

Rearranging the first equation gives 6A2 - 29A + 35 = 0, which factors into (2A - 5)(3A - 7) = 0, yielding A = 5/2 (which is 2.5) and A = 7/3 (which is 2.33). The second equation simplifies to 10B2 - 161B + 624 = 0, which factors into (2B - 13)(5B - 48) = 0, yielding B = 6.5 and B = 9.6. Comparing these real values shows that both values of A are smaller than both values of B, so A < B.

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