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Let f(x) = ax^(2) - bx + c^(2), b ne 0 a...

Let `f(x) = ax^(2) - bx + c^(2), b ne 0 and f(x) ne 0` for all `x in R`. Then

A

`a + c^(2) lt b`

B

`4a + c^(2) gt 2b`

C

`9a - 3b + c^(2) lt 0`

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
2
Here, `x^(2) - bx + c^(2) = 0` does not have real roots. So,
`D lt 0 rArr b^(2) - 4ac^(2) lt 0 rArr a gt 0`
Therefore, f(x) is always positive. So,
`f(2) gt 0 rArr 4a - 2b + c^(2) gt 0`
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