Given that t<span>here
are 20 light bulbs in 5 packages.
The table to find the rate
that gives you the number of light bulbs in 3 packages is given as follows:
![\begin{tabular} {|c|c|c|c|c|c|} Light bulbs&4&8&12&16&20\\[1ex] Packages&1&2&3&4&5 \end{tabular}](https://tex.z-dn.net/?f=%5Cbegin%7Btabular%7D%0A%7B%7Cc%7Cc%7Cc%7Cc%7Cc%7Cc%7C%7D%0ALight%20bulbs%264%268%2612%2616%2620%5C%5C%5B1ex%5D%0APackages%261%262%263%264%265%0A%5Cend%7Btabular%7D)
Three different ways in which the rate can be written are:
12 light bulbs to 3 packages
12 light bulbs : 3 packages
12 light bulbs / 3 packages
</span>
For this case we have the following quadratic equation:

Where:

By definition, the discriminant of a quadratic equation is given by:

We have to:
Two different real roots
Two different complex roots
Two equal real roots
Substituting the values we have:

So, we have two different complex roots
Answer:
Two different complex roots
Step-by-step explanation:
<em><u>Hamiltonian function, also called Hamiltonian, mathematical definition introduced in 1835 by Sir William Rowan Hamilton </u></em>
We are given with the function <span>(sinx)/(1 + sinx). To simplify the equation, we multiply the denominator with its conjugate. Hence the expression becomes (</span>sinx)(1-sin x )/(1 + <span>sinx)(1-sin x). Then we convert the expression into </span>(<span>sinx)(1-sin x )/ cos^2 x. Using trigonometric functions, we can then simplify the expression.</span>