Question

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find the range of 'a' for which :

1. ax^2 + 3x +4 > 0

for all x belongs to R

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Answer 1

SOLUTION ::

Clearly a # 0

Now

ax² + 3x +4 > 0

➙ 1/4a [ 4a²x² + 12ax + 16a ] > 0

➙ 1/4a [ (2ax + 3 ) ² - 9 + 16a ] > 0

So Above inequality holds if

a > 0 & - 9+16a > 0

➙ a > 0 & 16a > 9

➙ a > 0 & a > 9/16

Combining we get

a > 9/16

Which is the required range for a

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Answer 2

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