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For all ' x^(prime),x^2+2a x+(10-3a)>0, ...

For all `' x^(prime),x^2+2a x+(10-3a)>0,` then the interval in which `' a '` lies is

A

`a lt -5`

B

`-5 lt a lt 2`

C

a gt 5`

D

2 lt a lt5`

Text Solution

Verified by Experts

The correct Answer is:
B
As we know, `ax^(2)+bx+x gt0` for all `x in R,` iff `a gt 0 and D lt 0.`
Given equation is `x^(2)+2ax+(10-2a)gt0, AAx inR`
Now, `D lt0`
`implies4a^(2)-4(10-3a)lt0`
`implies4(a^(2)+3a-10)lt0`
`(a+5) (a-2) lt0impliesa in (-5,2)`
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