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
oksian1 [2.3K]
3 years ago
14

What are the real and complex solutions of the polynomial equation? x^4-41x^2=-400. *work needed*

Mathematics
1 answer:
pickupchik [31]3 years ago
6 0
<h3>Answer: x = -5, -4, 4 and 5.</h3><h3>All four zeros are real solutions.</h3>

Step-by-step explanation:

Given the polynomial equation x^4-41x^2=-400.

Adding 400 on both sides to get rid 400 from right side and set 0 on right side, we get

x^4-41x^2+400=-400+400.

x^4-41x^2+400=0.

Factoring by product sum rule.

We need product of 400 and sum upto -41.

We can see that 400 = -25 × -16 = 400 and -25-16 = -41.

Therefore,

x^4-25x^2-16x^2+400=0

Making it into two groups, we get

(x^4-25x^2)+(-16x^2+400)=0

Factoring out GCF of each group, we get

x^2(x^2-25)-16(x^2-25)=0

(x^2-25)(x^2-16) =0

Factoring out  (x^2-25) and (x^2-16) separately by difference of the squares identity a^2-b^2=(a-b)(a+b), we get

(x^2-25) = x^2-5^2= (x-5)(x+5) and

x^2-16 = x^2-4^2 =(x-4)(x+4).

Therefore,

(x-5)(x+5)(x-4)(x+4) =0

Applying zero product rule,

x-5=0

x+5=0

x-4=0 and

x+4=0.

Therefore,

<h3>x = -5, -4, 4 and 5.</h3><h3>All four zeros are real solutions.</h3>
You might be interested in
Find the volume of this prism 8cm to 9cm to 11cm
vladimir2022 [97]

Answer:

V = 792 m3

I am kinda guessing on this since you didn't provide a unit or label what the height, width, and length are. Also you should specify what prism...

7 0
3 years ago
Read 2 more answers
SOMEONE PLEASE HELP ME ASAP PLEASE!!!!​
ehidna [41]

Answer:

Therefore,

a_{21}=2

Step-by-step explanation:

Given:

A=\left[\begin{array}{ccc}3&6&9\\2&4&8\\\end{array}\right]

To Find:

a₂₁ = ?

Solution:

Let,

A=\left[\begin{array}{ccc}a_{11}&a_{12}&a_{13}\\a_{21}&a_{22}&a_{23}\\\end{array}\right]

We require  ' a₂₁ ' i.e Second Row First Column Element

So on Comparing we get

∴ a_{21}=2

Therefore,

a_{21}=2

5 0
2 years ago
Math help guys how wouls i work this out
Andrei [34K]

8 > 7 + \frac{x}{6}   Subtract 7 from both sides

1 > \frac{x}{6}   Multiply both sides by 6

6 > x   Flip it around so it's easier to read

x < 6

You can graph your answer by drawing an open circle at the 6 and coloring the line to the left. The circle should be open, because x is <em>less than 6</em>, not less than or equal to. You would color to the left to show that x can be anything less than 6.

4 0
3 years ago
What is (x2 + 9x+ 18) / (x+6)
ohaa [14]

Answer:

x+3

Step-by-step explanation:

7 0
3 years ago
Read 2 more answers
Evaluate the given algebraic expressions using the value of the variables:
lana66690 [7]

1. 6(3-8)-10

=6(-5)-10

=-30-10

=-40

2.30(3)+15(10)

=90+150

=240

3. 2(3)(3+32+32)

=6(67)

=402

4 0
3 years ago
Other questions:
  • D. The sum of two numbers is 30 and the difference of these numbers is 6.
    12·1 answer
  • A drawer contains 4 red socks, 7 white socks, and 11 blue socks. Without looking, you draw out a sock and then draw out a second
    6·1 answer
  • At 2.80 per pound,the cheddar cheese costs how many cents per pound ounce
    5·1 answer
  • Simplify the product using the distributive property. (5h - 5)(5h - 6)
    12·1 answer
  • I need help please.
    11·1 answer
  • Does anyone know the answer? thank you!​
    9·1 answer
  • What is the greatest common factor for 20y^9+5y^6
    11·1 answer
  • FREE BRAINLIEST!! ill also answer questions that you have posted if you answer correctly!!!! (30pts)
    9·1 answer
  • A local boys club sold 136 bags of mulch and made a total of $538. It sold two types of mulch: hardwood for $4.25 a bag and pine
    12·1 answer
  • 4x+4y=4 3x+y=10 solve by elimination
    14·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!