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swat32
3 years ago
5

Write a polynomial function of minimum degree with real coefficients whose zeros include those listed. Write the polynomial in s

tandard form.
5, -3, and -1 + 3i
Mathematics
1 answer:
sergey [27]3 years ago
8 0

Answer:

y = x⁴ − 9x² − 50x − 150

Step-by-step explanation:

Complex roots come in conjugate pairs.  So if -1 + 3i is a root, then -1 − 3i is also a root.

y = (x − 5) (x + 3) (x − (-1 + 3i)) (x − (-1 − 3i))

y = (x − 5) (x + 3) (x + 1 − 3i) (x + 1 + 3i)

Distribute using FOIL (first, outer, inner, last) to get real coefficients:

y = (x − 5) (x + 3) (x² + (1 + 3i)x + (1 − 3i)x + (1 − 3i)(1 + 3i))

y = (x − 5) (x + 3) (x² + x + 3ix + x − 3ix + 1 + 3i − 3i − 9i²)

y = (x − 5) (x + 3) (x² + 2x + 1 + 9)

y = (x − 5) (x + 3) (x² + 2x + 10)

Distribute to convert from factored form to standard form:

y = (x² + 3x − 5x − 15) (x² + 2x + 10)

y = (x² − 2x − 15) (x² + 2x + 10)

y = x²(x² + 2x + 10) − 2x(x² + 2x + 10) − 15(x² + 2x + 10)

y = x⁴ + 2x³ + 10x² − 2x³ − 4x² − 20x − 15x² − 30x − 150

y = x⁴ − 9x² − 50x − 150

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stiv31 [10]

Answer:

100000

Step-by-step explanation:

10x10x10x10x10= 100000

7 0
2 years ago
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Gemiola [76]

Answer:

A. (3, 8) and 2\sqrt{2}

B. (2, 4) and 2\sqrt{10}

Step-by-step explanation:

Midpoint formula: (\frac{x1+x2}{2} ,\frac{y1+y2}{2})

Distance formula: \sqrt{(x_{2}-x_{1}) ^2+(y_{2}-y_{1}) ^2 }

A. plug in the points in the formulas

(4, 7) and (2, 9)

Midpoint:

(\frac{4 + 2}{2} , \frac{7+9}{2} )=6/2, 16/2 = (3,8)

Length:

\sqrt{(2-4)^2+(9-7)^2}=\sqrt{4+4} =\sqrt{8} =2\sqrt{2}

B.

(5, 5) and (-1, 3)

Midpoint:

(\frac{5-1}{2} , \frac{5+3}{2} )=4/2,8/2=(2,4)

Length:

\sqrt{(-1-5)^2+(3-5)^2} =\sqrt{-6^2+-2^2} =\sqrt{36+4} =\sqrt{40} = 2\sqrt{10}

Can you consider marking my answers as brainliest lol it would mean a lot. Hope this helped.

4 0
2 years ago
Use the functions h(x) = 2x − 5 and t(x) = 6x + 4 to complete the function operations listed below.
Anika [276]
For this case we have the following functions:
 h (x) = 2x - 5
 t (x) = 6x + 4

 Part A: (h + t) (x)
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 Part B: (h ⋅ t) (x)
 (h ⋅ t) (x) = h (x) * t (x)
 (h ⋅ t) (x) = (2x - 5) * (6x + 4)
 (h ⋅ t) (x) = 12x ^ 2 + 8x - 30x - 20
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 Part C: h [t (x)]
 h [t (x)] = 2 (6x + 4) - 5
 h [t (x)] = 12x + 8 - 5
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6 0
3 years ago
Math math math math math <br> i need help<br> tysm :) &lt;3
stiv31 [10]

Answer:

C. x^14

Step-by-step explanation:

(x^9)^0 is 1

(x^7)^2 is x^14

x^14*1 is x^14

The Answer is C. x^14

Hope this helps!

5 0
2 years ago
Rounded to the nearest thousand of 275,608
olga nikolaevna [1]
The thousandths place in 275,608 is the 5. Depending on the next number (which in this case is the 6) it will either round up or down. Since the next number is 6 and it's 5 or bigger, the 5 will round up. So your final answer is 276,000.
4 0
3 years ago
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