Question
I. 2p2 + 5p + 2 = 0Â Â Â Â Â Â Â Â II.
2q2 + 11 q + 14 = 0 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.Solution
I. 2p2 + 5p + 2 = 0  (2p + 1) (p + 2) = 0  p = - (1/2) or -2  II. 2q2 + 11 q + 14 = 0  (q + 2) (2q + 7) = 0  q = -2 or - (7 /2)  Hence, p ≥ q  Alternate Method:  if signs of quadratic equation is +ve and +ve respectively then the roots of equation will be -ve and -ve. 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 = -2, -7/2 After comparing roots of quadratic eqution we can conclude that p ≥ q.
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