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Question

In each question two equations are provided. On the basis of these you have to find out the relation between p and q. Give answer.

I. 2p2 - 3p – 2 = 0 II. 2q2 - 11q + 15 = 0

A if p = q Correct Answer Incorrect Answer
B if p > q Correct Answer Incorrect Answer
C if q > p Correct Answer Incorrect Answer
D if p ≥ q Correct Answer Incorrect Answer
E if q ≥ p Correct Answer Incorrect Answer

Solution

I. 2p2- 3p – 2 = 0,
(2p + 1)( p - 2) = 0
p = - (1/2) or 2,
II. 2q2- 11q + 15 = 0
(2q - 5) (q - 3) = 0,
q = (5/2) or 3;
Hence, q > p.
Alternate Method:
if signs of quadratic equation is -ve and -ve respectively then the roots of equation will be -ve and +ve. (note: -ve sign will come in smaller root)
So, roots of first equation = p = -1/2, 2
if signs of quadratic equation is -ve and +ve respectively then the roots of equation will be +ve and +ve.
So, roots of second equation = q = 5/2, 3
After comparing roots of quadratic eqution we can conclude that q > p.

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