Solving quadratic equations is one of the main topics of this unit. Some quadratic equations can be solved with only one method, some can be solved with multiple methods, and some can’t be solved at all. Think about a task in your daily life that can be accomplished in a variety of ways. How do you decide the best course of action for accomplishing that task? How is this process like choosing a method for solving a quadratic equation that can be solved in multiple ways?

Hi there!

Many things we do in everyday life have a variety of ways we can go about accomplishing them, but we most often choose the most practical and efficient method.

Efficiency saves time and prevents over-complication, which may lead to errors.

We might need to identify the specifics of the task and its circumstances to be able to determine the most efficient method to do it.

Solving a quadratic equation, we also must think about the most efficient method that can lead us to the correct answer. And doing so, we must identify the circumstances of the equation; Can it be solved by factoring? Is it easy to factor? What form is this quadratic equation in?

For example, let's say we're given the equation (x-1)(x+2)=0. This is an equation in factored form. In these kinds of scenarios, we can easily solve by setting each term equal to 0 (the Zero Product Property). This is the most efficient method:

x-1=0 --> x=1

x+2=0 --> x=-2

I hope this helps!

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step-by-step explanation:

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p ÷ r = tan(x)

step-by-step explanation:

given that there is a figure below shows a right triangle: a right triangle is shown with hypotenuse equal to q units and the length of the legs equal to p units and r units.

graph is missing so i will create the graph as per given information.

the angle between the legs having lengths p units and q units is y degrees. the angle between the legs having lengths r units and q units is x degrees.

now we need to find about what is p ÷ r equal to.

so we can use trigonometric ratio tan(x)=[altitude]/[base] to find the value of p ÷ r, because p is the altitude and r is the base.

p ÷ r=tan(x)

hence final answer is p ÷ r=tan(x).