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Shkiper50 [21]
3 years ago
6

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

Mathematics
1 answer:
lesya692 [45]3 years ago
5 0

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)

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2 years ago
The percent of licensed U.S. drivers (from a recent year) that are female is 48.60. Of the females, 5.03% are age 19 and under;
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Answer:

a) 51.4

b) answer attached

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6 0
3 years ago
A baker made 20 pies. A Boy Scout troop buys one–fourth of his pies, a preschool teacher buys one–third of his pies, and a cater
n200080 [17]

Answer:

The number of pies does the baker have left is 15.

Step-by-step explanation:

Given : A baker made 20 pies. A Boy Scout troop buys one–fourth of his pies, a preschool teacher buys one–third of his pies, and a caterer buys one–sixth of his pies.

To find : How many pies does the baker have left?

Solution :

Let x be the number of pies does the baker have left.

According to question,

Number of pies buys,

One-fourth =\frac{1}{4}

One-third =\frac{1}{3}

One-sixth =\frac{1}{6}

i.e. x=20-(20\times \frac{1}{4}+20\times \frac{1}{3}+20\times \frac{1}{6})

x=20-(5+20\times \frac{1}{3}+10\times \frac{1}{3})

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The number of pies does the baker have left is 15.

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3 years ago
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Step-by-step explanation:

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Then you add and subtract; 5-168 is -163

Hope This Helps!!!

5 0
3 years ago
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