If a polynomial function f(x) has roots –8, 1, and 6i, what must also be a root of f(x)? A. –6

Mathematics

2 answers:

-BARSIC- [3]3 years ago

7 0

Answer:

B. –6i

Step-by-step explanation:

Complex roots come in pairs. The pairs are complex conjugates. If you have a+bi, then you will have a-bi

Since we have 6i, the other root must be -6i

anyanavicka [17]3 years ago

6 0

Answer:

-6i

Step-by-step explanation:

Complex roots always come in pairs, and those pairs are made up of a positive and a negative version. If 6i is a root, then its negative value, -6i, is also a root.

If you want to know the reasoning, it's along these lines: to even get a complex/imaginary root, we take the square root of a negative value. When you take the square root of any value, your answer is always "plus or minus" whatever the value is. The same thing holds for complex roots. In this case, the polynomial function likely factored to f(x) = (x+8)(x-1)(x^2+36). To solve that equation, you set every factor equal to zero and solve for the x's.

x + 8 = 0

x = -8

x - 1 = 0

x = 1

x^2 + 36 = 0

x^2 = -36 ... take the square root of both sides to get x alone

x = √-36 ... square root of an imaginary number produces the usual square root and an "i"

x = ±6i

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(6,3*10^-2)÷(2,1*10^4

nexus9112 [7]

Answer:

$3*10^{-6}$ or $0.000003$

Given expression:

$(6.3*10^{-2}) : (2.1*10^4)$

Simplify it in steps below:

$(6.3*10^{-2}) : (2.1*10^4) =$
$(6.3 :2.1)*(10^{-2}:10^4)=$
$3*(10^{-2-4})=$
$3*10^{-6}$ or $0.000003$

<u>Used properties:</u>

$\cfrac{ab}{cd}=\cfrac{a}{c}*\cfrac{b}{d}$

$a^b:a^c=a^{b-c}$

$a^{-b}=1/a^b$

7 0

1 year ago

Read 2 more answers

The probability mass function of X is f(x)= 1/6, x 1.2...,6 then find out the value

Mumz [18]

For the given probability mass function of X, the mean is 3.5 and the standard deviation is 1.708.

A discrete random variable X's probability mass function (PMF) is a function over its sample space that estimates the likelihood that X will have a given value. f(x)=P[X=x].
The total of all potential values for a random variable X, weighted by their relative probabilities, is known as the mean (or expected value E[X]) of that variable.
Mean(μ) = 1(1/6) + 2(1/6) + 3(1/6) + 4(1/6) + 5(1/6) + 6(1/6).
Mean(μ) = (1+2+3+4+5+6)/6
Mean(μ) = 21/6
Mean(μ) = 3.5
The square root of the variance of a random variable, sample, statistical population, data collection, or probability distribution represents its standard deviation. It is denoted by 'σ'.
A random variable's variance (or Var[X]) is a measurement of the range of potential values. It is, by definition, the squared expectation of the distance between X and μ. It is denoted by 'σ²'.
σ² = E[X²]−μ²
σ² = [1²(1/6) + 2²(1/6) + 3²(1/6) + 4²(1/6) + 5²(1/6) + 6²(1/6)] - (3.5)²
σ² = [(1² + 2²+ 3² + 4²+ 5²+ 6²)/6] - (3.5)²
σ² = [(1 + 4 + 9 + 16 + 25 + 36)/6] - (3.5)²
σ² = (91/6) - (3.5)²
σ² = 15.167-12.25
σ² = 2.917
σ = √2.917
Standard deviation (σ) = 1.708