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kompoz [17]
3 years ago
6

Write a polynomial function of least degree with integral coefficients that has the given zeros

Mathematics
1 answer:
Zigmanuir [339]3 years ago
6 0

Answer:

x^{4} + 3x² - 4

Step-by-step explanation:

Note that complex zeros occur in conjugate pairs

If 2i is a zero then - 2i is a zero

The zeros are x = 1, x = - 1, x = 2i, x = - 2i, thus the factors are

(x - 1), (x + 1), (x - 2i) and (x + 2i)

The polynomial is expressed as the product of the factors, thus

f(x) = (x - 1)(x + 1)(x - 2i)(x + 2i) ← expanding in pairs

     = (x² - 1)(x² - 4i²) → i² = - 1

     = (x² - 1)(x² + 4) ← distribute

     = x^{4} + 4x² - x² - 4

     = x^{4} + 3x² - 4

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Let f(x) = 12 over the quantity of 4 x + 2. Find f(−1). (1 point)
mylen [45]

Answer:

-6

Step-by-step explanation:

Hope I understand your "f(x) = 12 over the quantity of 4 x + 2" correctly

f(x) = 12 / 4x +2

Now so they want a f(-1), as u can see they substituted the x for - 1, therefor do that the same to the right side

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3 years ago
Write an equation of a line that passes through the point (4,3) and is perpendicular to the graph of the equation y=−13x+4.
lilavasa [31]

Answer:

y = -13x + 55

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perpendicular formula : m1 × m2 = -1

y = -13x + 4

now we take the grafient of the equation which is 13 :

m × 13 = -1

m = -13

so now we hv a new gradient then we can find the equation use the formula y = mx + c :

m = -13 point = ( 4 , 3 )

sub them into the formula,

3 = -13 (4) + c

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55 = c

c = 55

now we rewrite again the c and the m to become a complete equation : y = -13x + 55

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Which of these statements is true?
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