Question

hello guys
________________

find the range of a for which:

ax^2 + 4x -2 < 0

for all x belongs to R

__________________

plz don't spam..

answer needed
​

Answer 1

SOLUTION ::

Clearly a # 0

Now

ax² + 4x - 2 < 0

➙ 1/4a [ 4a²x² + 16ax - 8a ] < 0

➙ 1/4a [ (2ax + 4) ² - 16- 8a ] < 0

So Above inequality holds if

a > 0 & - 16-8a > 0

➙ a > 0 & - 8a > 16

➙ a > 0 & a < - 2

Combining we get

0 < a < - 2

Which is the required range for a

Please Mark it Brainliest

Answer 2

Answer:Clearly a # 0

Now

ax² + 4x - 2 < 0

➙ 1/4a [ 4a²x² + 16ax - 8a ] < 0

➙ 1/4a [ (2ax + 4) ² - 16- 8a ] < 0

So Above inequality holds if

a > 0 & - 16-8a > 0

➙ a > 0 & - 8a > 16

➙ a > 0 & a < - 2

Combining we get

0 < a < - 2

Which is the required range for a