Question

polynomials

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

(x-7)(x+11)(x-2-6i)=0

Answer 3

you forgot a factor ....

Answer 4

i get that it would be x^2+x-40 but how do i multiply that?

Answer 5

@amistre64

Answer 6

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

the first 2 are simple enough

the last 2 is just distribution

Answer 7

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

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

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

xx-2x+6xi -2x-2(-2)+6(-2)i -6xi-2(-6i) +6i(-6i)

x^2 -2x +6xi -2x +4 -12i -6x i+12i -36i^2

x^2 -2x +6xi -2x +4 -12i
-6x i +12i -36i^2
---------------------------------
x^2 -2x +4 -36i^2

but i^2 = -1 sooo

x^2 -2x +4 +36

Answer 8

okay so x^2+4x-77
and then -2x-6ix?

Answer 9

forgot a -2x in that last process :)

x^2 -4x +4 + 36

Answer 10

(x-7)(x+11) = x^2 +4x - 77

(x-(2+6i)) (x-(2-6i)) = x^2 -4x +40

now its just multiplication of again

Answer 11

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

Answer 12

wait. thats the second half? itd end up being like (-2x-6ix)(-2x+6ix)

Answer 13

it went from 2 problems into 3... what are doing /).(\

Answer 14

sites lagging .... good luck

Answer 15

so x^4-53x^2+468x-3080?

Answer 16

treat i like you would for any number except i^2=-1. i is the imaginary number and is the sqrt(-1)