First slide

Theory of equations

Question

If the equation $(3 x)^{2} + (27 \times 3^{1 / p} - 15) x + 4 = 0$ has equal roots, then $p =$

Moderate

A

0
B

2
C

--1/2
D

none of these

Solution

The given equation will have equal roots iff Disc = 0 $\begin{array}{l} \Rightarrow {(27 \times 3^{1 / p} - 15)}^{2} - 144 = 0 \\ \Rightarrow 27 \times 3^{1 / p} - 15 = \pm 12 \\ \Rightarrow 27 \times 3^{1 / p} = 27 or, 3 \\ \Rightarrow 3^{1 / p} = 1 or, 3^{1 / p} = \frac{1}{9} \Rightarrow \frac{1}{p} = 0 or - 2 \end{array}$
But, $1 / p$ cannot be zero. So, p = -1/2

Get Instant Solutions

When in doubt download our app. Now available Google Play Store- Doubts App

Recieve an sms with download link

Doubts App

OR

SCAN ME

Doubts App

Doubts App