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the less interger a , for which 1+...

the less interger a , for which
`1+log _(5)(x^(2)+1)le log_(5) (ax^(2)+4x+a)` is true for all `x in ` R is -

A

6

B

7

C

10

D

1

Text Solution

Verified by Experts

The correct Answer is:
B
inequality `ax^(2)+ 4x + a gt0` is possible if a gt0 and `16- 4a^(2)lt 0implies alt 2`
`log_(5)5 +log(x^(2)+1)lelog (ax^(2)+4x+a)`
` 5 (x^(2)+1) leax^(2)+4x+a`
` (a-5) x^(2)+4X +(a-5)gt 0` if hold if ` a-5gt 0` and `16-4 (a-5)^(2)ge0`
` agt 5 and a le 3 or , a ge 7 implies a le 7 a in [7,00)`
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