Question

Write a polynomial function if its leading coefficient is -3, and its roots include 4, 0 and 5x-2i.

Answer 1

Answer:

Step-by-step explanation:

Complex roots come in conjugates.  Your roots are

 

x = -3i

x= 3i

x = 2

x = -i

x = i

 

Since  i=√-1 , then i2=-1

 

For the root   x = 3i , we can say that the factor is  

 

(x - 3i)(x + 3i) = x2 - 9i2

                     = x2 - 9(-1)

                     = x2 + 9

 

(x - i)(x + i) = x2 - i2

                 = x2 + 1

 

 

Then your polynomial is

 

f(x) = (x - 2)(x2 + 1)(x2 + 9)

Answer 2

Answer:

• See below

Step-by-step explanation:

Given a polynomial with:

• The leading coefficient is - 3
• Roots are 4, 0, 5 - 2i

We know the complex roots should be paired with their conjugate.

So 5 + 2i is also a root.

The least polynomial is:

f(x) = - 3(x - 4)(x - 0)(x - 5 - 2i)(x - 5 + 2i) =

         -3x(x - 4)(x² - 10x + 29) =

         -3x(x³ - 14x² + 69x - 116) =

         -3x⁴ + 42x³ - 207x² + 348x