Multiple choice

Directions: In the question given below, equations I and II are given. You have to solve both the equations and give answer. I. 16p2 - 22p + 7 = 0 II. 14q2 + q - 4 = 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
A Correct answer
Explanation

Solving the first quadratic equation gives the roots p = 1/2 and p = 7/8. Solving the second quadratic equation gives the roots q = 1/2 and q = -4/7. Comparing the values, we find that p is always greater than or equal to q.

AI explanation

Factor the first equation 16p squared minus 22p plus 7 equals 0 to find its roots, which are 7 divided by 8 and 1 divided by 2. Factor the second equation 14q squared plus q minus 4 equals 0 by splitting the middle term, which gives the roots 1 divided by 2 and negative 4 divided by 7. Comparing the roots, the maximum value of p is 7 divided by 8 and the minimum value of p is 1 divided by 2, while the maximum value of q is 1 divided by 2 and the minimum is negative 4 divided by 7. Since p can be greater than q or equal to q, the relationship is p is greater than or equal to q.

Keep practicing — related questions