The possible values of n for which the equation nx2+(2 n - 1)x+(n - 1)=0 has roots of opposite sign is/are given by

Question

The possible values of n for which the equation nx2+(2 n - 1)x+(n - 1)=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

Tardigrade Admin · Accepted Answer

D=(2 n - 1)2-4n(n - 1)=4n2+1-4n-4n2+4n=1>0 Product of roots =(n - 1/n) < 0 ⇒ n(n - 1) < 0 ⇒ n∈ (0 , 1)

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

no values of $n$

all values of $n$

$- 1 < n < 0$

$0 < n < 1$

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

Q. The possible values of n for which the equation nx2+(2n−1)x+(n−1)=0 has roots of opposite sign is/are given by

no values of n

all values of n

−1<n<0

0<n<1