Question

Help asap****
Which polynomial function has a leading coefficient of 1 and roots (7 + i) and (5 – i) with multiplicity 1?

f(x) = (x + 7)(x – i)(x + 5)(x + i)
f(x) = (x – 7)(x – i)(x – 5)(x + i)
f(x) = (x – (7 – i))(x – (5 + i))(x – (7 + i))(x – (5 – i))
f(x) = (x + (7 – i))(x + (5 + i))(x + (7 + i))(x + (5 – i))

Answer 1

Complex roots come in conjugate pairs, meaning if (7 + i) is a root, then (7 - i) is also a root, and if (5 - i) is a root, then (5 + i) is also a root.

So the four roots are (7 + i), (7 - i), (5 - i), and (5 + i). Subtract each of them from x and multiply the factors to get the polynomial

Answer 2

So im thinking the third choice fits your description. because you have (x-(7-i))

Answer 3

yes that's right

Answer 4

rather than just 7-x

Answer 5

Would you be able to help me with a similar one

Answer 6

ok

Answer 7

If a polynomial function f(x) has roots –9 and 7 – i, what must be a factor of f(x)?

you would do the same thing right? like (x + (7 + i)) ?

Answer 8

yeah, but it's always "x - ___" so (x - (7 + i))

Answer 9

Its x- for every problem like that?

Answer 10

yes. even for real roots. You'd represent the root of -9 as (x - (-9)) or (x + 9)

Answer 11

Which second degree polynomial function has a leading coefficient of –1 and root 4 with multiplicity 2?
f(x) = –x^2 – 8x – 16
f(x) = –x^2 + 8x – 16
f(x) = –x^2 – 8x + 16
f(x) = –x^2 + 8x + 16

Answer 12

how do you find the multiplicity?

Answer 13

Multiplicity is the exponent on the factor. A root of 4 means the factor is (x - 4). Multiplicity of 2 means that (x - 4) is a factor twice and it should be written as (x - 4)². A leading coefficient of -1 means the function is y = -(x - 4)².

I'd multiply/expand -(x - 4)² to see which choice it matches