Answer-I. 2p2 - 3p &ndash; 2 = 0&nbsp; &nbsp; &nbsp; &n...

Q: Answer-&lt;p&gt;I. 2p&lt;sup&gt;2&lt;/sup&gt; - 3p &amp;ndash; 2 = 0&amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;n...

I. 2p2 - 3p ndash 2 0, 2p 1 p - 2 0 p - 12 or 2, II. 2q2 - 11q 15 0 2q - 5 q - 3 0, q 52 or 3 Hence, q gt 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 -12, 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 52, 3 After comparing roots of quadratic eqution we can conclude that q gt p.

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Question

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

A if p = q Correct Incorrect

B if p > q Correct Incorrect

C if q > p Correct Incorrect

D if p ≥ q Correct Incorrect

E if q ≥ p Correct Incorrect

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

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