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The domain of $f (x) = l n (a x^{3} + (a + b) x^{2} + (b + c) x + c),$ where $a > 0, b^{2} - 4 a c = 0,$ is (where [.] represents greatest integer function)

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-1,∞--b2a

1,∞--b2a

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Correct option is A

We must have ax3+a+bx2+b+cx+c>0or ax2x+1+bxx+1+cx+1>0or x+1ax2+bx+c>0or ax+1x+b2a2>0 as b2=4acor x>-1 and x≠-b2a

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The domain of fx=lnax3+a+bx2+b+cx+c, where a>0, b2-4ac=0, is (where [.] represents greatest integer function)

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The domain of $f (x) = l n (a x^{3} + (a + b) x^{2} + (b + c) x + c),$ where $a > 0, b^{2} - 4 a c = 0,$ is (where [.] represents greatest integer function)