Write an inequality that represents the statement A number r is at most 11

Find all the zeros of the polynomial function p(x) = x3 – 5x2 + 33x – 29

hram777 [196]

Answer:

$\large \boxed{\sf \ \ x=1, \ \ x=2+5i, \ \ x=2-5i \ \ }$

Step-by-step explanation:

Hello,

I assume that we are working in $\mathbb{C}$ , otherwise there is only one zero which is 1. Please consider the following.

First of all, <u>we can notice that 1 is a trivial solution</u> as

$p(1) = 1^3-5\cdot 1^2 + 33\cdot 1-29=1-5+33-29=0$

It means that (x-1) is a factor of p(x) so we can find two real numbers, a and b, so that we can write the following.

$p(x)=(x-1)(x^2+ax+b)=x^3+ax^2+bx-x^2-ax-b=x^3+(a-1)x^2+(b-a)x-b$

Let's identify like terms as below.

a-1 = -5 <=> a = -5 + 1 = -4

b-a = 33

-b = -29 <=> b = 29

So

$\boxed{ \ p(x)=(x-1)(x^2-4x+29) \ }$

Now, we need to find the zeroes of the second factor, meaning finding x so that:

$x^2-4x+29=0 \ \text{ complete the square, 29 = 25 + 4} \\ \\ x^2-2\cdot 2 \cdot x+2^2+25=0 \\ \\ (x-2)^2=-25=(5i)^2 \ \text{ take the root } \\ \\x-2=\pm 5i \ \text{ add 2 } \\ \\ x = 2+5i \ \text{ or } \ x = 2-5i$

Hope this helps.

Do not hesitate if you need further explanation.

Thank you

5 0

3 years ago

Which of the following systems of linear inequalities is represented by the

algol [13]

Answer:

Option D is correct.

Step-by-step explanation:

Option D is correct.

y < 2 and y >= x

Because the dotted line shows that y < 2 and y >=x is shown is represented by diagonal line.

5 0

3 years ago

Read 2 more answers

Which expression can be placed on the right side of the equals sign to form an equation 2+33=

qaws [65]

Answer: 33+2, 32+3, 31+4, 30+5, 29+6, 28+7, 27+8, 26+9, 25+10, 24+11, 23+12, 22+13, 21+14, 20+15, 19+16, 18+17, 17+18, 16+19, 15+20, 14+21, 13+22, 12+23, 11+24, 10+25, 9+26, 8+27, 7+28, 6+29, 5+30, 4+31, 3+32, 1+34.

Step-by-step explanation: Plz give e brainliest

5 0

3 years ago

What is the standard form equation of the line shown below?

nadya68 [22]

Answer: Choice A

x+3y = 14

======================================================

Explanation:

The general template for standard form is Ax+By = C, where A,B,C are integers.

This immediately rules out choices C and D, since they don't fit the format mentioned.

To see which of A or B we can eliminate or confirm, plug (x,y) coordinates from the graph into each answer choice. The ultimate goal is to get a true statement.

For example, the graph shows that (x,y) = (2,4) is on the line. Plug this into choice A to get...

x+3y = 14

2+3(4) = 14

2+12 = 14

14 = 14 this is true

So far so good. The point (2,4) is on the line x+3y = 14. Repeat those steps for (-1, 5) and you should get another true result. So that would confirm choice A is the answer. You only need a minimum of two points to define a unique line, meaning we only need to verify two points on the line. Anything more is just extra busy work.

---------

If we tried (2,4) with choice B, then,

5x+3y = 14

5(2)+3(4) = 14

10+12 = 14

22 = 14 which is false

This indicates (2,4) is not on the line 5x+3y = 14. We can rule out choice B because of this.

3 0

3 years ago

Read 2 more answers

PLEASE HELP I ONLY HAVE AN HOUR posting again because I really need an answer

Firlakuza [10]

The answer to your question is C

4 0

3 years ago