All categories

2 years ago

1. If a polynomial of Degree 4 has an imaginary zero at -2i and a real zero at 5, how many imaginary zeros does it have?

Mathematics

1 answer:

Vadim26 [7]2 years ago

4 0

Answer:

Complex roots for polynomials equations will always come in conjugate pairs. Since 1-2i is a root, 1+2i will also be a root. (Just switch the sign of the imaginary part to its opposite.)

Step-by-step explanation:

So far we have 1-2i and 1+2i as roots. We need two more to make a 4th degree polynomial.

x=1 with multiplicity of 2 means that we count the root twice when we write down the polynomial: (x - 1)(x - 1) = (x - 1)2

Putting it all together, we can construct our polynomial of degree 4 as

y = f(x) = (x - 1)(x - 1)[x - (1-2i)][x - (1+2i)]

Multiply the factors (FOIL):

[x - (1-2i)][x - (1+2i)] =

x2 - (1+2i)x - (1-2i)x + (1-2i)(1+2i) =

x2 - x - 2ix - x + 2ix + (1 + 2i - 2i + 4) =

x2 - 2x + 5

(x - 1)(x - 1) = x2 - x - x + 1 = x2 - 2x + 1

Now multiply the two underlined expressions:

y = (x2 - 2x + 5)(x2 - 2x + 1)

= x4 - 2x3 + 5x2 - 2x3 + 4x2 - 10x + x2 - 2x + 5 by multiplying term by term

= x4 - 4x3 + 10x2 -12x + 5 by collecting like terms.

You might be interested in

Complete the number sentence to show an example of the Distributive Property.

galben [10]

The answer would be 18

Hope that helps.

3 0

3 years ago

Is the relationship between red and blue marbles additive or multiplicative? Write the

natali 33 [55]

D I just took the test

8 0

3 years ago

Which power has a base of 2 and an<br> exponent of 6?<br> A 28<br> B 62<br> C 126

Mashcka [7]

Answer:

Step-by-step explanation:

the base is the the big number, the exponent the small one

8 0

3 years ago

Read 2 more answers

3. You roll two fair dice, a white one and a red one. (a) Find P(5 or 6 on the white die and an odd number on the red die) (b) F

Elden [556K]

Answer:

a. P(5 or 6 on the white die and an odd number on the red die) = 1/6

b. P(odd number on the white die and 5 or 6 on the red die) = 1/6

c. P(5 or 6 on the white die and an odd number on the red die) or P(odd number on the white die and 5 or 6 on the red die) = 1/3

Step-by-step explanation:

(a) P(5 or 6 on the white die and an odd number on the red die)

Step 1: P(5 or 6 on the white die) = 1/6 + 1/6 = 1/3

Step 2: P(odd number on the red die) = 1/2

Step 3: P(5 or 6 on the white die and an odd number on the red die) = 1/3 × 1/2 = 1/6

(b) Find P(odd number on the white die and 5 or 6 on the red die).

Step 1: P(odd number on the white die) = 1/2

Step 2: P(5 or 6 on the red die) = 1/6 + 1/6 = 1/3

Step 3: P(odd number on the white die and 5 or 6 on the red die) = 1/2 × 1/3 = 1/6

(c) Find P(5 or 6 on the white die and an odd number on the red die) or P(odd number on the white die and 5 or 6 on the red die).

Step 1: P(5 or 6 on the white die and an odd number on the red die) = 1/6

Step 2: P(odd number on the white die and 5 or 6 on the red die) = 1/6

Step 3: P(5 or 6 on the white die and an odd number on the red die) or P(odd number on the white die and 5 or 6 on the red die) = 1/6 + 1/6 = 1/3

7 0

2 years ago

A salesperson works 40 hours per week at a job where she has two options for being paid. Option A is an hourly wage of $28. Opt

Karolina [17]

Option b!!!!!!!!!!!!!

6 0

2 years ago