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anonymous
 one year ago
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))
anonymous
 one year ago
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))

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anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Complex 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

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0So im thinking the third choice fits your description. because you have (x(7i))

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0rather than just 7x

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Would you be able to help me with a similar one

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0If 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)) ?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0yeah, but it's always "x  ___" so (x  (7 + i))

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Its x for every problem like that?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0yes. even for real roots. You'd represent the root of 9 as (x  (9)) or (x + 9)

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Which 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

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0how do you find the multiplicity?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Multiplicity 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
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