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Question

# If 5p2−7p−3=0 and 5q2−7q−3=0, p≠q, then the equation whose roots are 5p−4q and 5q−4p is :

A
5x2+x439=0
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B
5x2+7x439=0
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C
5x27x439=0
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D
5x2+7x+439=0
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Solution

## The correct option is C 5x2−7x−439=05p2−7p−3=0 and 5q2−7q−3=0 So p,q are the roots of the equation of 5x2−7x−3=0 ⇒p+q=75, pq=−35 Let a=5p−4q, b=5q−4p be the roots of a new quadratic equation. So, sum of roots, a+b=5(p+q)−4(p+q)⇒a+b=p+q=75 Product of roots, ab=(5p−4q)(5q−4p) ⇒ab=41pq−20(p2+q2)⇒ab=41pq−20(p+q)2+40pq⇒ab=81pq−20(p+q)2=−4395 Hence, the required equation is 5x2−7x−439=0

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