All categories

4 years ago

If 5+6i is a root of the polynomial function f(x),which of the following must also be a root of f(x)

2 answers:

4 0

The complex conjugate root theorem states that if a+bi (with a and b being numbers) is a root, then a-bi is also a root. Plugging that in here, this means that 5-6i is also a root

Lubov Fominskaja [6]4 years ago

4 0

Answer:

5 - 6i must also be a root of f(x)

Step-by-step explanation:

Complex conjugates states that the two complex numbers are conjugates of each other if they have the same real part and their imaginary parts are negatives of each other i.e, the complex conjugate of a + bi is a - bi where i is imaginary.

Conjugate root theorem states that if the complex number a + bi is a root of a polynomial P(x) in one variable with real coefficients, then the complex conjugate a-bi is also a root of that polynomial.

Given: if 5+ 6i is a root of the polynomial function f(x).

then,

by the conjugate root theorem;

5 - 6i is also be a root of the polynomial f(x).

Read more on coordinate plane;

brainly.com/question/10737082

#SPJ1

3 0

2 years ago

M=y2-y1/X2-x1 solve y2

irinina [24]

      M      = (y₂ - y₁) / (x₂ - x₁)

Multiply each side by (x₂ - x₁):   M/(x₂ - x₁) = (y₂ - y₁)

Add y₁ to each side:       y₂ = M/(x₂ - x₁) + y₁

4 0

3 years ago

Suppose approximately 75% of all marketing personnel are extroverts, whereas about 70% of all computer programmers are introvert

Setler [38]

Answer:

$P(x \ge 5) = 1.000$ ---- At least 5 from marketing departments are extroverts

$P(x=15) = 0.013$ ---- All from marketing departments are extroverts

$P(x = 0) = 0.002$ ---------- None from computer programmers are introverts

Step-by-step explanation:

See comment for complete question

The question is an illustration of binomial probability where

$P(x) = ^nC_x * p^x * (1 - p)^{n-x}$

$(a):\ P(x \ge 5)$

$n = 15$ --- marketing personnel

$p = 75\%$ --- proportion that are extroverts

Using the complement rule, we have:

$P(x \ge 5) = 1 - P(x < 5)$

So, we have:

$P(x < 5) =P(x = 0) + P(x = 1) + P(x = 2) + P(x = 3) + P(x = 4)$

$P(x = 0) = ^{15}C_{0} * (75\%)^0 * (1 - 75\%)^{15 - 0} = 1 * 1 * (0.25)^{15} = 9.31 * 10^{-10}$

$P(x = 1) = ^{15}C_{1} * (75\%)^1 * (1 - 75\%)^{15 - 1} = 15* (0.75)^1 * (0.25)^{14} = 4.19 * 10^{-8}$

$P(x = 2) = ^{15}C_{2} * (75\%)^2 * (1 - 75\%)^{15 - 2} = 105* (0.75)^2 * (0.25)^{13} = 8.80 * 10^{-7}$

$P(x = 3) = ^{15}C_{3} * (75\%)^3 * (1 - 75\%)^{15 - 3} = 455* (0.75)^2 * (0.25)^{12} = 0.0000153$

$P(x = 4) = ^{15}C_{4} * (75\%)^4 * (1 - 75\%)^{15 - 4} = 1365 * (0.75)^4 * (0.25)^{11} = 0.000103$

So, we have:

$P(x < 5) = (9.31 * 10^{-10}) + (4.19 * 10^{-8}) + (8.80 * 10^{-7}) + 0.0000153 + 0.000103$

$P(x < 5) = 0.00011922283$

Recall that:

$P(x \ge 5) = 1 - P(x < 5)$

$P(x \ge 5) = 1 - 0.00011922283$

$P(x \ge 5) = 0.9998$

$P(x \ge 5) = 1.000$ --- approximated

$(b)\ P(x = 15)$

$n = 15$ --- marketing personnel

$p = 75\%$ --- proportion that are extroverts

So, we have:

$P(x) = ^nC_x * p^x * (1 - p)^{n-x}$

$P(x=15) = ^{15}C_{15} * 0.75^{15} * (1 - 0.75)^{15-15}$

$P(x=15) = 1 * 0.75^{15} * (0.25)^{0$

$P(x=15) = 0.013$

$(c)\ P(x = 0)$

$n=5$ ---------- computer programmers

$p = 70\%$ --- proportion that are introverts

So, we have:

$P(x) = ^nC_x * p^x * (1 - p)^{n-x}$

$P(x = 0) = ^{5}C_0 * (70\%)^0 * (1 - 70\%)^{5-0}$

$P(x = 0) = 1 * 1 * (0.30)^5$

$P(x = 0) = 0.002$

3 0

3 years ago

What is the general form of the given polynomial?

True [87]

A general polynomial of one variable could have any number of terms. If this is what you were asking for then I hope this helps!

5 0

3 years ago

Finding Inverses<br> Find an equation for the inve<br> 3.<br> y = 3x + 2

Kipish [7]

First we swap our x and y variable, so we get

x = 3y + 2

Then, we solve for y
We can first subtract 2 on both sides

x - 2 = 3y

Then we can divide by 3 on both sides to get

x/3 - 2/3 = y

So our final equation is

y = x/3 - 2/3

7 0

3 years ago