If the equation `(3x)^(2)+(27 xx 3^(1//p)-15) x + 4 = 0` has equal roots, then p =

Options

A. 0
B. 2
C. `-1//2`
D. none of these

Answer

C

Explanation

The given equation will have equal roots iff Disc = 0
`rArr" "(27 xx 3^(1//p)-15)^(2) - 144 = 0`
`rArr" "27 xx 3^(1//p) - 15 = +- 12`
`rArr" "27 xx 3^(1//p) = 27 or, 3`
`rArr" "3^(1//p) = 1 or, 3^(1//p) =(1)/(9) rArr (1)/(p)=0 or -2`
But, 1/p cannot be zero. So, p = - 1/2