Question

write a polynomial function with the following features: it has three distinct zeros: one of the zeros is 1; another zero has a multiplicity of 2.

Answer 1

multiplicity of 2 I think this means the same number twice (x-n)^2
with a zero of 1 then (x-1) is a factor

Answer 2

@campbell_st does it mean (x-2)^2 is a factor? need to check

Answer 3

if x = 1 is a zero then (x-1) is a factor

multiplicity of 2 means the zero is repeated twice...

and you need one more zero, call is c as the question says 3 distinct.

Answer 4

that's correct.... x = 2 is a zero with multiplicity 2... so it only touches the x-axis and doesn't cut it.

Answer 5

So could the answer be y=(x-1)(x-2)^2?

Answer 6

no... you need another factor that isn't (x-1) or (x-2)^2 as it says you need 3 distinct.

so pick a number

Answer 7

So would (2x-4) work for the third distinct number?

Answer 8

no... as that is the same as 2(x -2)

so if I said x = -5 is a zero... what would the factor be..?

Answer 9

(x+5)?

Answer 10

Okay. So, would y=(x-1)(x-2)^2(x+5) work?