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Question

In the given questions, you will find two equations labeled as I and II. solve both equations and determine the accurate relationship between the variables 'p' and 'q'. Choose the correct option based on your analysis of the solutions.

I. 2p2 + 25p – 13 = 0

II. 2q2 – 19q = 2q + 23

A p > q Correct Answer Incorrect Answer
B p < q Correct Answer Incorrect Answer
C p ≥ q Correct Answer Incorrect Answer
D p = q or the relationship cannot be established Correct Answer Incorrect Answer
E p ≤ q Correct Answer Incorrect Answer

Solution

ATQ, From I: 2p2 + 25p – 13 = 0 Or, 2p2 + 26p – p – 13 = 0 Or, 2p(p + 13) – 1(p + 13) = 0 Or, (2p – 1)(p + 13) = 0 Or, p = (1/2), -13 From II: 2q2 – 19q = 2q + 23 Or, 2q2 – 19q – 2q – 23 = 0 Or, 2q2 – 21q – 23 = 0 Or, 2q2 – 23q + 2q – 23 = 0 Or, q(2q – 23) +1(2q – 23) = 0 Or, (2q – 23)(q + 1) = 0 Or, q = (23/2) or -1 So, no relation can be established between ‘p’ and ‘q’

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