Answer-&nbsp;I. p2 +7p + 10 = 0&nbsp; &nbsp; &nbsp; &nb...

Q: Answer-&lt;p&gt;&amp;nbsp;I. p&lt;sup&gt;2&lt;/sup&gt; +7p + 10 = 0&amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nb...

I. p2 7p 10 0, p2 5p 2p 10 6 0 or p p5 2 p5 0 p2 p5 0, or p -2 or -5, II. q2 - q ndash 6 0 q2 ndash 3q 2q ndash 6 0 qq-3 2q -3 0 or, q -2 or 3 Hence, q ge p 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 -2, -5 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 second equation q -2, 3 After comparing roots of quadratic eqution we can conclude that q ge p.

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Question

I. p2 +7p + 10 = 0
II. q2 - q – 6 = 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. p² +7p + 10 = 0,

p²+ 5p + 2p + 10 + 6 = 0; or

p( p+5) + 2( p+5) = 0

(p+2)( p+5) = 0, or p = -2 or = -5,

II. q² - q – 6 = 0;

q² – 3q + 2q – 6 = 0

q(q-3) + 2(q -3) = 0 or, q = -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.

So, roots of first equation = p = -2, -5

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 second equation = q = -2, 3

After comparing roots of quadratic eqution we can conclude that q ≥ p.

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I. p2 +7p + 10 = 0II. q2 - q – 6 = 0

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I. p2 +7p + 10 = 0
II. q2 - q – 6 = 0