If #x=1+i# is a factor of #ax^2+bx+c# then what is another factor?

Answer 1

c) #1-i#

I'll presume that you meant "zero" or "root" when you said "factor."

A 'factor' would be something like #(x - 1 - i)#, which corresponds to a 'zero' #x=1+i# of #ax^2+bx+c#, also called a 'root' of #ax^2+bx+c = 0#.
If #x = 1+i# is a zero of #ax^2+bx+c# and #a#, #b# and #c# are Real numbers then #x = 1-i# is the other zero.
If #a#, #b# and #c# can be Complex numbers, then the other zero can be anything.

Generally speaking, zeros in any polynomial with real coefficients are either real or occur in pairs of complex conjugates.

From the perspective of the Real numbers, there is no way to tell the difference between #i# and #-i#. The only thing the Real numbers 'know' about #+-i# is that they are square roots of #-1#.
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Answer 2

If (x = 1 + i) is a factor of (ax^2 + bx + c), then its complex conjugate (x = 1 - i) will also be a factor.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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