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Grace [21]
3 years ago
12

Do you know what the answer to this question is?

Mathematics
1 answer:
Y_Kistochka [10]3 years ago
3 0

I think the answer is 4

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Find an​ nth-degree polynomial function with real coefficients satisfying the given conditions.
lesya692 [45]

Answer:

\displaystyle f(x) = -2(x-2)(x^2+4)

Step-by-step explanation:

We want to find a third degree polynomial with zeros <em>x </em>= 2 and <em>x</em> = 2i and f(-1) = 30.

First, note that by the Complex Root Theorem, since <em>x</em> = 2i is a root, <em>x</em> = -2i must also be a root.

Hence, we will have the three factors:

\displaystyle f(x) = a(x-(2))(x-(2i))(x-(-2i))

Where <em>a</em> is the leading coefficient.

Expand and simplify the second and third factors:

\displaystyle \begin{aligned} (x-(2i))(x-(-2i)) &= (x-2i)(x+2i) \\ \\ &= x(x-2i)+2i(x-2i) \\ \\ &= (x^2 - 2ix) + (2ix - 4i^2) \\ \\ &=x^2 + 4\end{aligned}

Hence:

\displaystyle f(x) = a(x-2)(x^2+4)

Since f(-1) = 30:

\displaystyle \begin{aligned}  f(x) &= a(x-2)(x^2+4) \\ \\ (30) &= a((-1)-2)((-1)^2+4) \\ \\ 30 &= -15a \\ \\ a&= -2\end{aligned}

In conclusion, third degree polynomial function is:

\displaystyle f(x) = -2(x-2)(x^2+4)

5 0
3 years ago
Need quick answers has to show work
Zielflug [23.3K]

Answer:

Step-by-step explanation:

For some read I can’t see the pictures

8 0
3 years ago
A ball is launched into the sky at 272 feet per second from the roof of a skyscraper 1,344 feet tall. The equation for the ball’
xz_007 [3.2K]

When the ball is in the ground, its height is basically equal to zero thus making our equation,

<span>    -16t^2 + 272t + 1344 = 0</span>

Simplifying the equation will give us,

<span>  - t^2 + 17t + 84 = 0 or t^2 – 17t – 84 = 0</span>

Factoring out the equation will give us,

<span>   (t – 21)(t + 4) = 0</span>

Thus, t = 21 or t = -4. -4 is an extraneous root. Thus, the answer is t = 21.

<span>Answer: 21 seconds</span>

5 0
3 years ago
When renting a limo for prom, the number of people varies inversely with the cost per person. Originally there were 12 people an
pashok25 [27]
The answer would be $10.
8 0
3 years ago
Complete the equation describing how x and y are related.
Sav [38]

Answer: The "?" would equal 1.

Step-by-step explanation: This is simply a line with a slope of 1 and a y-intercept of zero.

5 0
2 years ago
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