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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. p2+ 2p – 8 = 0 II. q2 – 5q + 6 = 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. p2+ 2p – 8 = 0
⇒ (p + 4) ( p – 2) = 0
⇒ p = 2, - 4
II. q2– 5q + 6 = 0
⇒ ( q - 3) ( q - 2) = 0
⇒ q = 2, 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 larger root)
So, roots of first equation = p = 2, -4
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 = 2, 3
After comparing roots of quadratic eqution we can conclude that q ≥ p.

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