Choose the letter of the correct answer. Write the chosen letter on a separate sheet of paper.

Mathematics

1 answer:

Daniel [21]3 years ago

7 0

Answer:

1. A

2. B

3. B

4. C

5. A

Step-by-step explanation:

1. Data: is referred to as the collection of facts such as values and measurement. It include but isn't limited to attributes, names, fields and definitions that are being used in a computer database system.

2. Quantitative: this nature of data can be classified as discrete or continuous data. It is typically based on numerical values such as mathematical or statistical analysis of data gathered or collected from various sources e.g questionnaires, polls, surveys etc.

3. Sample: it is a sub-collection of elements coming from a certain population. Sampling can be defined as a process used to collect or select data (objects, observations, or individuals) from a larger statistical population using specific procedures.

4. Black, blue, yellow, and red are examples of what qualitative data according to its nature. It includes variables that are non-numerical in nature i.e they are categorical. For example, the color of a car, gender, shapes etc.

5. Juan conducted his research using a survey method because he created a questionnaire so as to gather data from his participants.

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These roots of the polynomial equation x^4-4x^3-2x^2+12x+9=0 are 3,-1,-1. Explain why the fourth root must be a real number. Fin

Alex787 [66]

Roots with imaginary parts always occur in conjugate pairs. Three of the four roots are known and they are all real, which means the fourth root must also be real.

Because we know 3 and -1 (multiplicity 2) are both roots, the last root $r$ is such that we can write

$x^4-4x^3-2x^2+12x+9=(x-3)(x+1)^2(x-r)$

There are a few ways we can go about finding $r$ , but the easiest way would be to consider only the constant term in the expansion of the right hand side. We don't have to actually compute the expansion, because we know by properties of multiplication that the constant term will be $(-3)(1)(1)(-r)=3r$ .

Meanwhile, on the left hand side, we see the constant term is supposed to be 9, which means we have

$3r=9\implies r=3$

so the missing root is 3.

Other things we could have tried that spring to mind:

- three rounds of division, dividing the quartic polynomial by $(x-3)$ , then by $(x+1)$ twice, and noting that the remainder upon each division should be 0