If $b^{2} - 4ac = 0$ and $a 0$, then domian of the function $f(x) = \log{\{(ax^{2} + bx + c)(x + 1)\}}$ is

Question

If $b^{2} - 4ac = 0$ and $a > 0$, then domian of the function $f(x) = \log{\{(ax^{2} + bx + c)(x + 1)\}}$ is

Dr. Abubacker · Accepted Answer

(c)
Given,
$\ \ \ f(x) = \log\left\{ \left( ax^{2} + bx + c \right)(x + 1) \right\}$
$\ \ \ \ \ \ \ \ \ \ \ \ \  = \log{\left( ax^{2} + bx + c \right) + \log{(x + 1)}}$
For $f(x)$ to be defined
$ax^{2} + bx + c > 0$ and $x + 1 > 0$
$\Rightarrow \ \ \ \ \ \ x > - 1$
Hence, option (c) is correct.

Q. If $b^{2} - 4ac = 0$ and $a > 0$, then domian of the function $f(x) = \log{\{(ax^{2} + bx + c)(x + 1)\}}$ is

Explanation

Reviewed by Dr. Abubacker

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