<PRE><B>Question 3222</B>
First, solve the equation:&lt;br&gt;
{{{x^2 + 4x + 6 = 0}}}&lt;br&gt;
The equation has the form:&lt;br&gt;
{{{ax^2 + bx + c = 0}}}, where a = 1, b = 4 and c =6&lt;br&gt;
This problem does not have neat factors, so we apply the quadratic equation:&lt;br&gt;
{{{(-b +- sqrt(b^2 - 4ac))/(2a))}}}&lt;br&gt;
Using the values for a, b and c we just identified, the quadratic equation becomes:&lt;br&gt;
{{{(-4 +- sqrt(4^2 - 4*6))/2 = (-4 +- sqrt(16 - 24))/2 = (-4 +- sqrt(-8))/2}}}&lt;br&gt;
This is a complex number! To find where this equation is less than 3 depends on what you mean by less than when talking about complex numbers.&lt;br&gt;
To answer this correctly, I would ask you to verify the equation then I would ask you to define less than for complex numbers.&lt;br&gt;
In any case, the roots of the equation are:&lt;br&gt;
{{{-2 +- sqrt(-2) = -2 + sqrt(2)i}}} and {{{-2 - sqrt(2)i}}}&lt;br&gt;</PRE>