Question

Having troubles please help!

Answer 1

Write a polynomial function of minimum degree with real coefficients whose zeros include those listed. Write the polynomial in standard form.

7, -11, and 2 + 6i

Answer 2

Are you supposed to multiply them all together?
Like (x+7)(x-11)(2+6i)?

Answer 3

1. When a polynomial has real coefficients and complex zeros, the complex zeros come in conjugate pairs.
2. The factors with zeros are this way. If "a" is a zero, the factor is (x - a), not (x + a). For example, if -4 is a zero, the factor that has it is (x - (-4)) = (x + 4).
3. The complex zeros are the same way. If you have 1 +2i as a zero, its factor will be (x - (1 + 2i)) = (x - 1 - 2i)
4. Once you figure out all factors, then you do multiply them.

Answer 4

So would it be f(x) = x^4 - 117x^2 + 468x - 3080 ?

Answer 5

@mathstudent55

Answer 6

how did you get there so fast?

Answer 7

I worked it out and that is the answer I came to. Is it the correct answer?

Answer 8

the -3080 is correct, meaning you used the right numbers, but all your other terms are off.

what you multiplied together should be (x+7)(x-11)(2+6i)(2-6i)

therefore the highest degree of you have is 2, or x^2. idk where the x^4 in yours came from

Answer 9

The coefficient of x is wrong. The rest is correct.

Answer 10

in essence what you are actually multiplying is 40(x+7)(x-11)

because the (2+6i)(2-6i) = 40

Answer 11

@funinabox What?
The polynomial is this product:
(x - 7)(x + 11)(x - (2 + 6i))(x - (2 - 6i))

Answer 12

what @mathstudent55 put is what I worked out, but I guess I did it worng? so my coeffcient for x is worng?

Answer 13

Yes, that's the only thing that's off. Everything else you have is correct.

Answer 14

alright well did you do it to get (x^2-4x+77)(x^2-4x+6i-6i)?
I think I got it wrong becasue I am having diffculties wit hthe imaginary numbers

Answer 15

i do not think that is correct.

Answer 16

x^4 - 9x^3 - 42x^2 + 234x - 3080
is what I got this time.

Answer 17

(x - 7)(x + 11)(x - (2 + 6i))(x - (2 - 6i))
(x^2 - 7x + 11x - 77)(x - 2 - 6i)(x - 2 + 6i)

Answer 18

(x^2 + 4x - 77)( (x - 2)^2 - (6i)^2 )
(x^2 + 4x - 77)(x^2 - 4x + 4 + 36)
(x^2 + 4x - 77)(x^2 - 4x + 40)

Answer 19

x^4 - 4x^3 + 40x^2 +4x^3 - 16x^2 + 160x - 77x^2 + 308x - 3080
x^4 - 53x^2 + 468x - 3080

Answer 20

oh okay I see how you got that. Man I was way off. Thank you for your help.

Answer 21

Did you understand this part:
(x - 2 - 6i)(x - 2 + 6i)
= ( (x - 2)^2 - (6i)^2 )

Answer 22

Your first answer was very close. You only had one coefficient off.

Answer 23

Yes but I was a little fuzzy on how you went from ( (x - 2)^2 - (6i)^2 ) to (x^2 - 4x + 4 + 36). When you square does it cancel the imaginary number out? like 6i^2=6i*6i=36