Which of the following are roots of the polynomial function? Check all that apply.

Mathematics

1 answer:

lutik1710 [3]3 years ago

8 0

You know 1 is not a root because the sum of the coeffcients of the equation is 14, not zero.

It is fairly easy to try 3 by synthetic division (see attachment), which tells you that 3 is a root and the remaining quadratic factor is x²-3x-5. The quadratic formula tells you the roots of that factor are

... x = (-b±√(b²-4ac))/(2a) = (3±√29)/2

The appropriate choices are

... C. (3-√29)/2

... D. (3+√29)/2

... F. 3

_____

The quadratic formula tells you the solution to

... ax²+bx+c=0

is x = (-b±√(b²-4ac))/(2a)

We have a=1, b=-3, c=-5.

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In order to solve this problem, we will need a little more information, for example, we need to know what the functions are. Let's say the problem looks like this:

Use the drawing tool(s) to form the correct answer on the provided number line. Consider the functions below.

$f(x)=|3x|-3$

and

$g(x)=-x^{2}+8x-5$

Represent the interval where both functions are increasing on the number line provided.

Answer:

See attached picture

Step-by-step explanation:

Since this problem is posted on the algebra section of Brainly, I assume we will need to make use of an algebraic approach to solve this. Basically, the idea is to graph the functions and find the x-values for which both functions increas. In order to graph the functions, we will need to build a table with points for each of the functions. In order to graph the functions you need to pick the x-values you wish and evaluate them in the given functions. (See attached pictures)

Once you got the desired points, you can plot them in the coordinate axis and find the x-values for which both graphs will be increasing. If we take a close look at the graphs we can see the f(x) graph increases in the interval:

(0,∞)

and the g(x) graph increases in the interval:

(-∞,4)

so the interval in which both graphs are increasing will be the region where both intervals cross each other, which will be (0,4)

so that's the interval we draw on our number line. (see attached picture.