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Reptile [31]
3 years ago
12

How many complex zeros does the polynomial function have? f(x)=−3x^6−2x^4+5x+6

Mathematics
1 answer:
REY [17]3 years ago
7 0

one way would be to factor

I can't factor it so we will have to use Descartes' Rule of Signs which is helpful for finding how many real roots you have


it goes like this:

for a polynomial with real coefients, consider f(x)=-3x^6-2x^4+5x+6.

after arranging the terms in decending order in terms of degree, count how many times the signs of the coeffients change direction and minus 2 from that number until you get to 1 or 0. that will be the number of even roots the function can have

We have (-, -, +, +). the signs changed 1 times, so it has 1 real positive root


to get the negative roots, we evaluate f(-x) and see how many times the root changes

f(-x)=-3x^6-2x^4-5x+6

signs are (-, -, -, +). there was 1 change in sign

so the function has 1 real negative root



a total of 2 real roots


a function of degree n can have at most, n roots


our function is degree 6 so it has 6 roots

if 2 are real, then the others must be complex

6-2=4 so there are 4 complex roots


you can also show that there are only 2 real roots by using a graphing utility to see that there are only 2 real roots

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Answer:

Y' = 360ex+ 30e

Step-by-step explanation:

Y=e×6x×(6x+1) × 5

y'= d/dx (e×6x ×(6x+1)×5)

y'=d/dx(30ex ×(6x+1))

y'=d/dx(180ex^2 + 30ex)

y'=d/dx(180ex^2) + d/dx (30ex)

Calculate the derivative

y'=180e×2x +30e

y'=360ex+30e

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3 years ago
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Graph -3x + 9y = -27​
Svetllana [295]

Answer:

Step-by-step explanation:

The first step you want to do is get one variable by itself. We are going to start by isolating y by itself.

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By isolating y by itself, you now have a function written in slope-intercept form. To graph this function, you can draw a point at (0,-3), then use rise/run to go up 1 unit and over 3 units to the next point (3,-2). You can then draw a line based on this information.

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miskamm [114]

Answer:

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Step-by-step explanation:

The standard equation of a circle is expressed as;

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Hence the radius of the circle is 2√3

7 0
3 years ago
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