In the following question, there are two equations. Solve them and give answer
I. 20P2 + 31P + 12 = 0
II. 21Q2 + 23Q + 6 = 0
Solution
Correct Answer: Option A
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 = \(- \frac{3}{7}\;,\; - \frac{2}{3}\)
⇒ Q = - 0.43, -0.66
On taking Q = - 0.43
⇒ P < Q (for both the values of P) . . . . equation 1
On taking Q = −0.66−0.66
⇒ P < Q (for both the values of P) . . . . equation 2
From equation 1 and 2
P < Q
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