Question

If the inequality $(m-2)x^2+8x+m+4>0$ is satisfied for all $xϵR$, then least integral m is

• A. $4$
• B. $5$
• C. $6$
• D. None of these

Answer 1

The correct option is A $4$

$(m-2)x^2+8x+m+4>0$

$b^2-4ac>0$

${\left(8\right)}^2-4(m-2)(m+4)>0$

$64-4(m^2-2m-8)>0$

$64-4m^2+8m+32>0$

$-4m^2+8m+96>0$

$-m^2+2m+24>0$

$-m^2-6m+4m+24>0$

$-m(m+6)+4(m+6)>0$

$(4-m)(m+6)>0$

The least integral of m is $4$.