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The domain of f(x)=ln(a x^3+(a+b)x^2+(b+...

The domain of `f(x)=ln(a x^3+(a+b)x^2+(b+c)x+c),` where `a >0, b^2-4ac=0`, is

A

`(-1,oo)~{-(b)/(2a)}`

B

`(1,oo)~{-(b)/(2a)}`

C

`(-1,1)~{-(b)/(2a)}`

D

None of these

Text Solution

Verified by Experts

The correct Answer is:
A
We must have `a x^(3)+(a+b)x^(2)+(b+c)x+c gt 0`
or ` ax^(2)(x+1)+bx(x+1)+c(x+1) gt 0`
or `(x+1)(ax^(2)+bx+c) gt 0`
or ` a(x+1)(x+(b)/(2a))^(2) gt 0 " as " b^(2)=4ac`
or `x gt -1 " and " x ne -(b)/(2a)`
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