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uranmaximum [27]
3 years ago
12

How many complex roots does the equation below have? X^6+x^3+1=0

Mathematics
2 answers:
gladu [14]3 years ago
7 0
If you find the discriminant it will tell you the number and types of roots. The discriminant is the value b^2 -4ac.
a = 1
b = 1
c = 1
1^2 - 4*1*1
1-4 = -3
Since this is a negative number there will be 2 complex roots.
solniwko [45]3 years ago
7 0

Answer:

The number of complex roots is 6.

Step-by-step explanation:

The given equation is

x^6+x^3+1=0

it can be written as

(x^3)^2+x^3+1=0

Substitute t=x^3,

(t)^2+t+1=0

Using quadratic formula.

t=\frac{-1\pm \sqrt{1^2-4(1)(1)}}{2}=\frac{-1\pm 3i}{2}     t=\frac{-b\pm \sqrt{b^2-4ac}}{2}

We know that

\omega =\frac{-1\pm 3i}{2}

It is a complex number.

x^3=\omega

x=(\omega)^{\frac{1}{3}}

Cube root of a complex number is complex.

Therefore the number of complex roots is 6.

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Answer:

C. 97.5 yd

Step-by-step explanation:

The distance between Marsha, the ball and the tee for the fourth hole, forms a triangle.

Thus, the distance between Marsha's ball and the hole can be calculated using the Cosine formula below:

c² = a² + b² - 2abcos(C)

Where,

c = distance between Marsha's ball and the hole = ?

a = distance between the tee for the fourth hole and the tee = 300 yd

b = distance between tee and the hole = 255 yd

C = 18°

c² = 300² + 255² - 2(300)(255)cos(18)

c² = 90000 + 65025 - 153000 × 0.951

c² = 155025 - 145503

c² = 9522

c = √9522 ≈ 97.5

c = distance between Marsha’s ball and the hole = 97.5 yd (nearest tenth)

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3 years ago
Write in slope intercept form an equation of the line that passes through the given points
Tpy6a [65]

Answer:

The desired equation is y = x + 8.

Step-by-step explanation:

As we move right from (-2,6) to (4,12), x increases by 6 and y also increases by 6.  Thus, the slope, m, m = rise / run, is m = 6/6, or just m = 1.

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The desired equation is y = x + 8.

4 0
3 years ago
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Answer:

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Step-by-step explanation:

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