Question

find the condition that the roots of the equation .x^2 - lx^2 +mx -n =0 may be in GP​

Answer 1

Let the two roots be 3α and 4α.

sum of roots=3α+4α=−

l

m

∴7α=−

l

m

∴α=−

7l

m

...(1)

product of roots=(3α)(4α)=

l

n

∴12α

2

=

l

n

Substituting the value of α from equation (1), we get

∴12(−

7l

m

)

2

=

l

n

∴

49l

2

12m

2

=

l

n

∴12m

2

=49nl