Question

Write a polynomial function of minimum degree with real coefficients whose zeros include those listed. Write the polynomial in standard form7, -11, and 2 + 6i :

Answer 1

f(x) = x4 - 53x2 + 468x - 3080

f(x) = x4 - 9x3 - 42x2 + 234x - 3080

f(x) = x4 - 117x2 + 468x - 3080

f(x) = x4 - 9x3 + 42x2 - 234x + 3080

Answer 2

@Hero

Answer 3

@Dbzfan836

Answer 4

@geerky42

Answer 5

im not good with these. I cant help you, dood. srry

Answer 6

@tkhunny

Answer 7

Write a polynomial function of minimum degree with real coefficients whose zeros include those listed. Write the polynomial in standard form7, -11, and 2 + 6i :

This is important: "minimum degree"

It means we must have a factor for each zero.

(x-7) and (x-(-11)) and (x-(2 + 6i))

This is important: " real coefficients"

It means any Complex zeros must come in conjugate pairs.

Okay, add this one: (x-(2 - 6i))

Answer 8

?

Answer 9

hmm is it -2x-61.. @tkhunny

Answer 10

im just gonna guess

Answer 11

You need to know what a factor is. This is why you have spent months and months studying factoring.

(x+2)(x+3) This has two factors. (x+2) and (x+3)

(x+2)(x+3)(x-1) This has three factors. (x+2) and (x+3) and (x-1)

To your problem:

This is important: "minimum degree"

It means we must have a factor for each zero, but no more than one.

(x-7) and (x-(-11)) and (x-(2 + 6i))

This is important: " real coefficients".

It means any Complex zeros must come in conjugate pairs.

Okay, add this one: (x-(2 - 6i))

This makes four factors all together.

(x-7) and (x-(-11)) and (x-(2 + 6i)) and (x-(2 - 6i))

Our polynomial is

(x-7)(x-(-11))(x-(2 + 6i))(x-(2 - 6i))

Simplified a little

(x-7)(x+11)(x-(2 + 6i))(x-(2 - 6i))

Multiply all that and you'll be done.