Multiple choice

Directions: Equations I and II are given. You have to solve both the equations and give answer. I. 21p2 - 19p + 4 = 0 II. 18q2 - 51q + 35 = 0

  1. p ≥ q

  2. p < q

  3. p > q

  4. p ≤ q

  5. p = q or relation cannot be established
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Solving 21p^2 - 19p + 4 = 0: roots are 4/7 and 1/3. Solving 18q^2 - 51q + 35 = 0: roots are 7/6 and 5/3. Comparing the values: 4/7 (approx 0.57) and 1/3 (approx 0.33) are both less than 7/6 (approx 1.16) and 5/3 (approx 1.66). Thus, p < q.

AI explanation

Factor the first equation 21p2 - 19p + 4 = 0 by splitting the middle term to get 21p2 - 12p - 7p + 4 = 0, which factors as (3p - 1)(7p - 4) = 0, giving the roots p = 1/3 and p = 4/7. Factoring the second equation 18q2 - 51q + 35 = 0 gives (3q - 5)(6q - 7) = 0, so the roots are q = 5/3 and q = 7/6. Comparing these real values on a number line shows that 1/3 and 4/7 are both less than 7/6 and 5/3, establishing that p is less than q.

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