Mathematics, 01.07.2019 00:10 AndiLizzi

what are the possible numbers of positive, negative, and complex zeros of f(x) = −3x4 −
5x3 − x2 − 8x + 4?
select one:
a. positive: 2 or 0; negative: 2 or 0; complex: 4 or 2 or 0
b. positive: 1; negative: 3 or 1; complex: 2 or 0
c. positive: 3 or 1; negative: 1; complex: 2 or 0
d. positive: 4 or 2 or 0; negative: 2 or 0; complex: 4 or 2 or 0

Answers: 1

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Answer from: rakanmadi87

Step-by-step explanation:

We have to look at sign changes in f(x) to determine the possible positive real roots.

f(x)=-3x^4-5x^3-x^2-8x+4

There is only one sign change here, between the -8x and the +4. So that means there is only 1 possible real positive root.

Now we have to look at sign changes in f(-x) to determine the possible negative real roots.

f(-x)=-3x^4+5x^3-x^2+8x+4

There are 3 sign changes here. That means there are either 3 negative roots or 3-2 = 1 negative root. So we have:

1 positive

3 or 1 negative

We need to pair them up now with all the possible combinations.

If we have 1 positive and 1 negative, we have to have 2 imaginary

If we have 1 positive and 3 negative, we have to have 0 imaginary

Keep in mind that the total number or roots--positive, negative, imaginary--have to add up to equal the degree of the polynomial. This is a 4th degree polynomial, so we will have 4 roots.

Answer from: Quest

x= -3 and $x=\frac{-3+/-3i\sqrt{3} }{2}$

step-by-step explanation:

to find the roots of a cubic, use division or factoring to find the factors then set equal to 0. as this is a difference of cubes, it factors into

$(x^3-a^3)=$ $(x-a)(x^2+ax+a^2)$

where a is the cube root of $a^3$ .

here this is 27 and the cube root of 27 is 3. so we write using the form:

$(x-3)(x^2+(3)x+3^2)\\(x-3)(x^2+3x+9)$ .

set each factor to 0 and solve for x.

x-3=0

x=3

the quadratic expression does not factor and must be solved using the quadratic formula.

$x=\frac{-b+/-\sqrt{b^2-4ac} }{2a}$

where a = 1, b=3, and c=9

$x=\frac{-3+/-\sqrt{3^2-4(1)(9)} }{2(1)} \\x=\frac{-3+/-\sqrt{9-36)} }{2} \\x=\frac{-3+/-\sqrt{-27)} }{2}\\x=\frac{-3+/-3i\sqrt{3} }{2}$

this cubic has two complex roots.

Answer from: Quest

when rotating a figure 180 degrees, imagine that you are able to take the figure and turn it clockwise or counterclockwise around a center point. to rotate a figure 180 degrees, you will need to apply the rule (x, y) → (-x, -y). start by using a coordinate grid with coordinates for each vertex of the figure. the center point of the coordinate grid is located at (0, 0), which is what you will rotate the figure around. write down the original coordinates of the shape you are going to rotate. then, apply the rule. for example, coordinate (1, 2) becomes (-1, -2). another example would be, coordinate (-4, -2) becoming (4, 2). after you change each original coordinate to the rotated coordinate, you will draw your new figure.

step-by-step explanation:

Identify the transformation that maps the figure with center (7, 1) onto itself. a) rotate 180° cloc

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what are the possible numbers of positive, negative, and complex zeros of f(x) = −3x4 −
5x3 −...

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