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. 12p2 - 35p + 18 = 0 II. 21q2 - 13q + 2 = 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
A Correct answer
Explanation

I: 12p^2 - 35p + 18 = 0. Roots: p = (35 +/- sqrt(1225 - 864)) / 24 = (35 +/- 19) / 24. p1 = 54/24 = 2.25, p2 = 16/24 = 0.66. II: 21q^2 - 13q + 2 = 0. Roots: q = (13 +/- sqrt(169 - 168)) / 42 = (13 +/- 1) / 42. q1 = 14/42 = 0.33, q2 = 12/42 = 0.28. Comparing roots, p > q.

AI explanation

Factoring the first equation, twelve p squared minus thirty five p plus eighteen equals zero, gives four p minus nine times three p minus two equals zero, which means p equals two point three three repeating or p equals zero point six six repeating. Factoring the second equation, twenty one q squared minus thirteen q plus two equals zero, gives seven q minus two times three q minus one equals zero, which means q equals zero point two eight repeating or q equals zero point three three repeating. Comparing the values, both roots of p are strictly greater than both roots of q. Therefore, p is greater than q.