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
adell [148]
3 years ago
10

What is the least possible degree of a polynomial that has roots -5,1 + 4i, and -4i?

Mathematics
1 answer:
Oksanka [162]3 years ago
6 0

Without any extra conditions, the answer could be 3, and the simplest polynomial with the given roots would be

(<em>x</em> + 5) (<em>x</em> - (1 + 4<em>i</em> )) (<em>x</em> + 4<em>i</em> )

= <em>x</em> ³ + 4<em>x</em> ² + (11 - 4<em>i</em> ) <em>x</em> + 80 - 2<em>i</em>

<em />

If the polynomial is supposed to have only <em>real</em> coefficients, then any complex roots must occur along with their complex conjugates:

(<em>x</em> + 5) (<em>x</em> - (1 + 4<em>i</em> )) (<em>x</em> - (1 - 4<em>i</em> )) (<em>x</em> + 4<em>i</em> ) (<em>x</em> - 4<em>i </em>)

= <em>x</em> ⁵ + 3<em>x</em> ⁴ + 23<em>x</em> ³ + 133<em>x</em> ² + 112<em>x</em> + 1360

and then the degree would be 5.

You might be interested in
HELP it's Geometry HW I WILL GIVE BRAIN LIST AND 5 STARS​
Margaret [11]
Number one: if line segments SR & RT are perpendicular line segment Tu and US are perpendicular and angle STR is congruent to angle TSU, then triangle TRS is congruent to triangle SUT
Number two: if line segment AC is congruent to line segment CB and line segment CB bisects line segment AB, then < a is congruent to < B
3 0
3 years ago
Use angle relationships to travel through the parallel maze following the prompts below.
musickatia [10]

Answer: 1,000,000,000,000,000,000,000,

Step-by-step explanation:

4 0
3 years ago
What's the area of the trapezoid
BlackZzzverrR [31]
46.5cm squared I believe
Hope this helped ;)

8 0
3 years ago
Can someone please help me i need this really bad.
nekit [7.7K]
The answer is the third one
6 0
3 years ago
Need help due tmr please and thank you :)
Katena32 [7]
10. After all the Pythagorean theorem the answer is 51.7215 cm
3 0
3 years ago
Other questions:
  • Write the conversion factor for converting meters to centimeters.
    11·2 answers
  • Solve the word problem. Mario has 18 coins in his drawer. Five of the coins are nickels, and the rest are pennies. What is the t
    9·1 answer
  • Perimeter with radius 14
    12·1 answer
  • 10. A person walks 12.0 m east, then turns and goes 5.00 m west, then turns and goes back 2.00 m east.
    12·1 answer
  • Help please I need help
    14·2 answers
  • Pls help 4!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
    10·1 answer
  • Three babies A, B and C cry out at every interval of
    5·2 answers
  • EXPLANATION?????
    6·2 answers
  • At the Planetarium, tickets cost $10 for adults and $5.50 for kids under 12. How
    8·1 answer
  • Help me Science Question
    11·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!