In the following question, there are two equations. Solve them and give answer I. 20P^2 + 31P + 12 = 0 II. 21Q^2 + 23Q + 6 = 0

A. P > Q
B. P < Q
C. P ≤ Q
D. P ≥ Q

Answer

B. P < Q

Solution

I. 20P²+31P+ 12 = 0

On doing factorization

20P²+15P+16P+12 = 0
5P (4P + 3) + 4 (4P + 3) = 0
(4P + 3) (5P + 4) = 0
P = -3/4, -4/5 P — 0.75, -0.80

II. 21Q² + 23Q + 6 = 0

On doing factorization

21Q² + 9Q + 14Q + 6 = 0
3Q (7Q + 3) + 2 (7Q + 3) = 0
(7Q + 3)(3Q + 2) = 0
Q = -3/7, -2/3 Q = – 0.43, -0.66

On taking Q = – 0.43

P < Q (for both the values of P) equation I

On taking Q = -0.66

P < Q (for both the values of P) equation II

From equation I and II
P < Q

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