Multiple choice

In each of the following questions two equations are given. You have to solve both the equation and find out the values of P and Q and $( (I) \quad 20P^2 + 31P + 12 = 0 \ (II) \quad 21Q^2 - 23Q + 6 = 0 )$

  1. If P > Q

  2. If P < Q

  3. If P ≥ Q

  4. If P ≤ Q

  5. P = Q or the relationship can not be established
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Solving equation (I): 20P² + 31P + 12 = 0. By factorization: (5P + 4)(4P + 3) = 0, so P = -4/5 = -0.8 or P = -3/4 = -0.75. Solving equation (II): 21Q² - 23Q + 6 = 0. By factorization: (7Q - 3)(3Q - 2) = 0, so Q = 3/7 ≈ 0.429 or Q = 2/3 ≈ 0.667. Comparing all values: Both P values (-0.8, -0.75) are less than both Q values (0.429, 0.667). Therefore P < Q is correct.

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