Question

The solution set for which the equation satisfies $[x^2+4x+3]+2x+5=0$:

• A. $(-1+\sqrt{3},-1-\sqrt{3})$
• B. $[-2,(-1+\sqrt{3}\left)\right]$
• C. $[-4,(-1-\sqrt{3}\left)\right]$
• D. None of these

Answer 1

The correct option is C $[-4,(-1-\sqrt{3}\left)\right]$

$\begin{array}{ccc}Consider& x^2+4x+3\ge 0& \dots \left(i\right)\\ then& (x^2+4x+3)+2x+5=0& \\ \Rightarrow & x=-2andx=-4& \end{array}$
but x = -2 does not satisfy eq (i)
$\begin{array}{ccc}Now,if& x^2+4x+3<0& \dots \left(ii\right)\\ then& -(x^2+4x+3)+2x+5=0& \\ \Rightarrow & x=-1-\sqrt{3}orx=-1+\sqrt{3}& \end{array}$
but only $x=-1-\sqrt{3}$ satisfies the eq. (ii).
Hence the solution set of x is $(-4,-1-\sqrt{3})$.

Alternatively:
Check the options by substituting the values from the options given in the question.