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if 3p^2=5p+2,3q^2=5q=2,p=!q,then the equation whose roots are 3p-2q and 3q-2p is?

if 3p^2=5p+2,3q^2=5q=2,p=!q,then the equation whose roots are 3p-2q and 3q-2p is?

Grade:Upto college level

1 Answers

SHAIK AASIF AHAMED
askIITians Faculty 74 Points
6 years ago
Hello student,
Please find the answer to your question below
Given roots are 3p-2q,3q-2p
hence sum of roots=p+q
product of roots=13pq-6(p2+q2)
so eqn is x2+(p+q)x+13pq-6(p2+q2)...................(1)
also given 3p2=5p+2..........(2) and 3q2=5q+2..............(3)
by subtracting 3 from 2 we get p+q=5/3
By adding 2 and 3 we get p2+q2=37/9
so pq=(p+q)2-(p2+q2)=-6/9
so from 1 the equation is 3x2+5x-100=0

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