Question

For each of the following sets of numbers, find the equation of a function that has these numbers as roots.

–3 + i and –3 – i

Answer 1

its 1

Answer 2

Find THE Equation. That is a horrible question.

1) There are infinitely many.
2) Are you SURE there are no requirements? Real Coefficients? Anything?

Answer 3

[x-(-3+i)] [x-(-3-i)]=0
(x+3-i)(x+3+i)=0
(x+3)^2 -(i)^2 =0
x2+6x+9+1=0
x2+6x+10+0

Answer 4

the last line should be
x2+6x+10=0

Answer 5

That is, indeed, one of the infinitely many possible answers to the question as it is stated.

Answer 6

well anything multiplied with x2+6x+10 is a solution. :)

Answer 7

@tkhunny the requirements are obviously real coefficients and being minimal degree.

Answer 8

No, that is not obvious. There is no such language in the problem statement. If we encourage the student to ignore necessary language, we do a grave disservice. If it is a requirement, it must be stated - hopefully clearly!

Answer 9

@tkhunny I'd agree with you but you're being pedantic. The context gives plenty of clues that this is obviously an elementary algebra or pre-calculus class and thus there is a VERY slim chance they're dealing with coefficients not in \(\mathbb{R}\)! :-) The degree thing I'll give you, though...

Answer 10

There is a very fine line between pedantic and necessary. I don't mind the risk. :-)

Answer 11

@oldrin.bataku BTW - how do you know what category a question is in. I never have that information!