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2 years ago

What is the least possible degree of a polynomial that has roots -5,1 + 4i, and -4i?

Mathematics

1 answer:

Oksanka [162]2 years ago

6 0

Without any extra conditions, the answer could be 3, and the simplest polynomial with the given roots would be

(x + 5) (x - (1 + 4i )) (x + 4i )

= x ³ + 4x ² + (11 - 4i ) x + 80 - 2i

If the polynomial is supposed to have only real coefficients, then any complex roots must occur along with their complex conjugates:

(x + 5) (x - (1 + 4i )) (x - (1 - 4i )) (x + 4i ) (x - 4i )

= x ⁵ + 3x ⁴ + 23x ³ + 133x ² + 112x + 1360

and then the degree would be 5.

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Serjik [45]

Step-by-step explanation:

$= \frac{ \frac{3}{x - 2} - 5 }{2 - \frac{4}{x - 2} }$

$= \frac{ \frac{3 - 5.(x - 2)}{x - 2} }{ \frac{2.(x - 2) - 4}{x - 2} }$

$= \frac{ \frac{3 - 5.(x - 2)}{ \cancel{x - 2}} }{ \frac{2.(x - 2) - 4}{ \cancel{x - 2} }}$

$= \frac{3 - 5.(x - 2)}{2.(x - 2) - 4}$

$= \frac{3 - 5x + 10}{2x - 4 - 4}$

$= \frac{ - 5x + 13}{2x - 8}$

$= \frac{13 - 5x}{2x - 8}$

The answer is D.

8 0

2 years ago

Evaluate the expression when x=7 and y=-3. 5y2-x

DIA [1.3K]

Answer:

-37

Step-by-step explanation:

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7 0

2 years ago

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Will choose brainliest... Figure out the combination...

Finger [1]

Answer:

Its THIS ↓↓↓↓

Step-by-step explanation:

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4 0

2 years ago

Read 2 more answers

If the area of a triangular kite is 6 square feet and its base is 4 feet, find the height

KonstantinChe [14]

The height of the kite is 3 feet. Here’s
why;
We know that BH=2A (base times height is equal to 2 times the area) of any given triangle.
Lets plug in values;
BH=2A
4(H)=2(6)
Then simplify;
4(H)=12
Flip the equation to find the missing value;
12 divided by 4 is 3.
Check your work;
4(3)=6(2):
12=12
The height of the kite is 3 feet.

4 0

2 years ago

Kazeer [188]

Answer:

C. quadratic function; quadratic term: −6x^2; linear term: −17x; constant term: −12

Step-by-step explanation:

Answer:

quadratic function; quadratic term: −6x² ; linear term: −17x; constant term: −12

Step-by-step explanation:

The given function is

We need to expand the RHS to get:

We can see that the degree of this polynomial function is 2 and hence it is a quadratic function.

The quadratic term is -6x²

The linear term is -17x

The constant term is -12

6 0

2 years ago