Question
Question: If the equation (3x)<sup>2</sup> + (27 × 3<sup>1/p</sup> – 15)x + 4 = 0 has equal roots, then p =...
If the equation (3x)2 + (27 × 31/p – 15)x + 4 = 0 has equal roots, then p =
A
0
B
2
C
–1/2
D
None of these
Answer
–1/2
Explanation
Solution
Here D = 0 (As eqn has equal roots)
so, (27 ×31/p–15)2 – 4 × 9 × 4 = 0
Ž 27×31/p – 15 = ± 12 , 27 × 31/p = 27 or 3 ;
i.e., 31/p = 1 or 31/p = 3–2
As 1/p cannot be zero, so p = –1/2