1.

For what value of n, the quadratic equation `3^(n)x^(2)+54x+81^(n)=0` have coincident roots?

Answer» We have,
`3^(n)x^(2)+54x+81^(n)=0`
For coincident roots, D=0
`implies(54)^(2)-4(3^(n))(81^(n))=0`
`implies4xx3^(n)xx3^(4n)=(54)^(2)implies3^(5n)=(54xx54)/(4)=729`
`implies3^(5n)=3^(6)implies5n=6impliesn=(6)/(5)`.


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