Question

The values of 'm' for which $(m-2)x^2+8x+(m+4)$ > 0 $\forall$ x $ϵ$ R, are

• A. m < –6 (or) m > 4
• B. m > 2
• C. m > 4
• D. can’t say

Answer 1

The correct option is C

m > 4

Let us draw graph as per the condition given i.e., y > 0 $\forall$ x $ϵ$ R where y = $(m-2)x^2+8x+(m+4)$

Here y > 0 $\forall$ x $ϵ$ R

Conditions are

i)a > 0

ii)D < 0

Reason: For graph to be above x-axis, D < 0 and a > 0.

a > 0 $\Rightarrow$ m - 2 > 0

m > 2 ....................(1)

D < 0 $\Rightarrow$ $b^2-4ac$ < 0

64 - 4(m - 2)(m + 4) < 0

(m - 2)(m + 4) > 16

$m^2+2m-8-16$ > 0

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

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

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

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

m < -6 $\cup$ m > 4............(2)

From (1) & (2),

m > 4