1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Mamont248 [21]
2 years ago
14

Find a polynomial function of degree 3 with 2, i, -i as zeros.

Mathematics
1 answer:
sergiy2304 [10]2 years ago
4 0

Answer:

p(x)= x^3-2x^2+x-2

Step-by-step explanation:

Here we are given that a polynomial has zeros as 2 , i and -i . We need to find out the cubic polynomial . In general we know that if \alpha , \ \beta \ \& \ \gamma are the zeros of the cubic polynomial , then ,

\sf \longrightarrow p(x)= (x -\alpha )(x-\beta)(x-\gamma)

Here in place of the Greek letters , substitute 2,i and -i , we get ,

\sf\longrightarrow p(x)= (x -2 )(x-i)(x+i)

Now multiply (x-i) and (x+i ) using the identity (a+b)(a-b)=a² - b² , we have ,

\sf  \longrightarrow p(x)= (x-2)\{ x^2 - (i)^2\}

Simplify using i = √-1 ,

\sf \longrightarrow p(x)= (x-2)( x^2 + 1 )

Multiply by distribution ,

\sf \longrightarrow p(x)= x(x^2+1) -2(x^2+1)

Simplify by opening the brackets ,

\sf\longrightarrow p(x)= x^3+x-2x^2-2

Rearrange ,

\sf\longrightarrow \underline{\boxed{\blue{\sf p(x)= x^3-2x^2+x-2}}}

You might be interested in
David drove the first six hours of his journey at 65 km/ hour and the last 3 hours of his journey at 80 km/hour how far is the w
zzz [600]
630 kilometers for the whole journey
4 0
3 years ago
Read 2 more answers
Ramandeep has a garden that is 6 and ⅔ feet by 7 and ⅘ feet. On the long side ¾ of the garden is planted and the remaining ¼ is
Ad libitum [116K]
1 2 3 4 your gonna get wrong hehehehehe
3 0
3 years ago
Read 2 more answers
What is the y intercept of x=14
Sophie [7]

Answer:

Step-by-step explanation:

x=14 is a vertical line with undefined slope

It has no y intercept and has only x intercept of 14.

6 0
3 years ago
Math help please show work thanks
katrin2010 [14]

Answer:

Total material needed = 9.5 square feet

Step-by-step explanation:

Dimensions  of I = 2. 5feet x 1 feet

    Area = 2.5 square feet

Dimensions of S :

                      Top part = 1 feet x 1 feet

                         Area of top part = 1 square feet

                      Bottom part = 1 feet x 2.5 feet

                          Area of bottom part = 2.5 square feet

  Total Area of S = 2.5 + 1  = 3.5  square feet

Total material needed = Area of I + Area of S + Area of S

                                  = 2.5 + 3.5 + 3.5

                                  = 9.5 square feet.

4 0
3 years ago
Findthe
Elanso [62]

Answer:

y- intercept = - 6

Step-by-step explanation:

The y- intercept is where the graph crosses the y- axis.

Let x = 0 and substitute in to the equation, that is

y = 0² - 3(0) - 6 = 0 - 0 - 6 = - 6 ← y- intercept

5 0
3 years ago
Other questions:
  • bracelet costs $8. Simone is also buying a necklace for her mother for $18. She believes that her total will be $98. Which expre
    10·2 answers
  • The value of the expression l-20l-l6l is
    13·1 answer
  • Describes the function y = -2 x + 5?
    11·1 answer
  • 6 yd<br> 11 yd<br> 16 yd<br> 5 yd<br> 13 yd
    6·1 answer
  • Two buses leave a station at the same time and travel in opposite directions. One bus travels
    15·1 answer
  • The length of a rectangular storage room is 5 feet longer than its width. If the area of the room is 104 square feet, find its d
    7·1 answer
  • <img src="https://tex.z-dn.net/?f=18-%5Csqrt%7B%7D%20-25" id="TexFormula1" title="18-\sqrt{} -25" alt="18-\sqrt{} -25" align="ab
    13·1 answer
  • Can you please help me with this question. ​
    8·1 answer
  • Please help me find the values!!! I need to submit this soon
    15·1 answer
  • What is the mean score Score<br> 90<br> 80<br> 70<br> 60
    13·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!