Multiple choice

Directions: In the following question, two equations numbered I and II are given. You have to solve both the equations and then choose the correct option. I. p2 - 49 = 0 II. 2q2 - 33q + 133 = 0

  1. p > q

  2. p ≥ q

  3. p < q

  4. p ≤ q

  5. p = q or no relation can be established

Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Solving I: p^2 = 49 gives p = 7 or p = -7. Solving II: 2q^2 - 33q + 133 = 0, using the quadratic formula, q = (33 +/- sqrt(1089 - 1064)) / 4 = (33 +/- 5) / 4, so q = 9.5 or q = 7. Comparing values, p <= q holds true.

AI explanation

Solving the first equation, p squared minus forty nine equals zero, gives p equals positive or negative seven. Factoring the second quadratic equation, two q squared minus thirty three q plus one hundred thirty three equals zero, yields two q minus nineteen times q minus seven equals zero, so q equals seven or q equals nine point five. Comparing the values, p can be positive seven or negative seven, while q can be seven or nine point five. Since positive seven is equal to seven and negative seven is less than seven, the relation p is less than or equal to q holds true.