Question

The possible values of $n$ for which the equation $nx^{2}+\left(2 n - 1\right)x+\left(n - 1\right)=0$ has roots of opposite sign is/are given by

• A. no values of $n$
• B. all values of $n$
• C. $-1 < n < 0$
• D. $0 < n < 1$

Answer 1

Answer: (D)

$D=\left(2 n - 1\right)^{2}-4n\left(n - 1\right)=4n^{2}+1-4n-4n^{2}+4n=1>0$
Product of roots $=\frac{n - 1}{n} < 0$
$\Rightarrow n\left(n - 1\right) < 0$
$\Rightarrow n\in \left(0 , 1\right)$