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max2010maxim [7]
3 years ago
12

Find the zeros (roots) of the following equations.

Mathematics
1 answer:
Ganezh [65]3 years ago
8 0

9514 1404 393

Answer:

  x ∈ {1/2, 1, 3, i, -i}

Step-by-step explanation:

We assume your function is supposed to be ...

  f(x) = 2x^5 -9x^4 +12x^3 -12x^2 +10x -3=0

I find it convenient to use a graphing calculator to find the real roots of higher-degree polynomials. The attached shows the real roots are ...

  x = 1/2, 1, 3

Factoring those out leaves the quadratic factor ...

  x^2 +1 = 0

That one has roots ±i.

So, the full complement of roots is ...

  x ∈ {1/2, 1, 3, i, -i}

_____

Descartes' rule of signs tells you the real roots are all positive. The rational root theorem tells you that rational roots are in the set {1/2, 1, 3/2, 3}. The sum of coefficients is 0, telling you that x=1 is a real root.

Factoring that from the polynomial leaves the 4th-degree factor ...

  2x^4 −7x^3 +5x^2 −7x +3 . . . . . division shown in 2nd attachment

For x=1, this has a negative value (-4), so you know there is a root between f(0) =3 and f(1) = -4. The only rational choice is 1/2.

Similarly, factoring that from the polynomial (along with a factor of 2) leaves the cubic ...

  x^3 -3x^2 +x -3 . . . . . division shown in 3rd attachment

This is clearly factorable by grouping to (x -3)(x^2 +1), so we have our third real root and the quadratic that yields the complex roots.

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More than 5 sides have octagons and hexagons
so 
8+14=22
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5 0
3 years ago
I NEED HELP!! I GO TO BED IN 10 MINUTES AND THIS ASSIGNMENT LOCKS TONIGHT!!!
77julia77 [94]

Answer:

y − 1 = -2 (x − 3)

Step-by-step explanation:

Point slope form is:

y − y₁ = m (x − x₁)

where m is the slope and (x₁, y₁) is a point on the line.

Given that m = -2 and (x₁, y₁) = (3, 1):

y − 1 = -2 (x − 3)

3 0
3 years ago
How do I find the center & radius, then write a standard equation for a,b, and c?
Ghella [55]

Firstly , we will locate centres and radius in the figures

(a)

We can see that

centre=(h,k)=(0,0)

radius=r=5

now, we can use standard equation of circle

(x-h)^2+(y-k)^2=r^2

we can plug values

we get

(x-0)^2+(y-0)^2=5^2

x^2+y^2=25

(b)

We can see that

centre=(h,k)=(5,4)

radius=r=3

now, we can use standard equation of circle

(x-h)^2+(y-k)^2=r^2

we can plug values

we get

(x-5)^2+(y-4)^2=3^2

(x-5)^2+(y-4)^2=9

(c)

We can see that

centre=(h,k)=(4,3)

radius=r=5

now, we can use standard equation of circle

(x-h)^2+(y-k)^2=r^2

we can plug values

we get

(x-4)^2+(y-3)^2=5^2

(x-4)^2+(y-3)^2=25


5 0
3 years ago
Ming wrote the table of points below.
anzhelika [568]

Answer:

Ming has described a proportional relationship because the ordered pairs are linear and the line passes through the origin

Step-by-step explanation:

Given

x - y

5 - 10

10 - 20

15 - 30

Required

Determine if the data are proportional

The dataset is small; so, we can derive the relationship by observation.

By observing the x and y values, the relationship is:

y = 2x --- i.e. multiply x values by 2.

This is further proven by:

y = 2 * 5 = 10

y = 2 * 10 = 20

y = 2 * 15 = 30

y = 2 * 0 = 0 --- the origin

Hence, the dataset is proportional and it passes through the origin.

7 0
3 years ago
TH
V125BC [204]
80 minutes because 8•10=80
8 0
3 years ago
Read 2 more answers
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