Question

I dont understand how to do this AT ALL! so can you help me kind of step by step that would be great!

Answer 1

1. Find the polynomial function with roots 1, –2, and 5.
2. Find the polynomial function with roots 1, 7, and –3 of multiplicity 2.
3. Find the polynomial function with roots 11 and 2i.

Answer 2

@aaronq

Answer 3

a polynomial with roots "dog", "moon", "something" can be written as\[P(x)=(x-dog)(x-moon)(x-something)\]

Answer 4

when a number like "a" (complex or real no matter what it is) is a root of polynomial P(x) then (x-a) is a factor of P(x)

Answer 5

suppose 4 is a root of polynomial Q(x) with multiplicity of 2 then\[(x-4)^2\]is a factor of Q(x)

Answer 6

okay so for the first one its
P(x) = (x - 1)(x + 2)(x - 5) ?

Answer 7

very right :)

Answer 8

second one:
P(x) = (x - 1)(x - 7)(2x + 9) ?

Answer 9

Third one:
P(x) = (x - 11)(x - 2i) ?

Answer 10

emm multiplicity of 2 for root -3 means u have 2 factors like (x+3) then ur polynomial for second example will be\[P(x)=(x-1)(x-7)\color\red{(x+3)(x+3)}\]\[P(x)=(x-1)(x-7)\color\red{(x+3)^2}\]third is right again :)

Answer 11

ohh okay makes sense

Answer 12

thank you (:!

Answer 13

very welcome :)