Question

Find $m$ for which $m{x}^2+(2m-1)x+m-1=0$ has roots of opposites sign.

• A. $\frac{1}{4}$
• B. $\frac{5}{2}$
• C. $\frac{3}{2}$
• D. $\frac{1}{2}$

Answer 1

Answer: (D)

$\frac{1}{2}$

According to given question,

$m{x}^2+(2m-1)x+m-1=0$

$⟹m{x}^2+mx+(m-1)x+m-1=0$

$⟹mx(x+1)+(m-1)(x+1)=0$

$⟹(x+1)(mx+m-1)=0$

$⟹mx+m-1=0$ ……..(1)

And, $⟹x+1=0⟹x=-1$

Hence , other root is $1$

Put, $x=1$ in eq. (1), we get

$2m-1=0$

$⟹m=\frac{1}{2}$