The domain of `f(x)=1n(a x^3+(a+b)x^2+(b+c)x+c),` where `a >0,b^2-4a c=0,i s(w h e r e[dot]` represetns greatest integer function). `(-1,oo)~(-b/(2a))` (1,`oo)~{-b/(2a)}` `(-1,1)~{-b/(2a)}` `non eoft h e s e`

Options

A. `(-1,oo)~{-(b)/(2a)}`
B. `(1,oo)~{-(b)/(2a)}`
C. `(-1,1)~{-(b)/(2a)}`
D. None of these

Answer

A

Explanation

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)`