Question

If the roots of the equation $(m-2)x^2-(8-2m)x-(8-3m)=0$ are real and opposite in sign, then the number of integral value(s) of $m$ is

• A. $0$
• B. $1$
• C. $2$
• D. more than $2$

Answer 1

The correct option is A $0$

$(m-2)x^2-(8-2m)x-(8-3m)=0$
Since, roots are opposite in sign, hence $0$ lies between the roots.
$\Rightarrow a\cdot f\left(0\right)<0$
$\Rightarrow (m-2)(3m-8)<0$
$\Rightarrow m\in (2,\frac{8}{3})$
Hence, no integral value of $m$ in this interval.