Question

Find a quadratic equation with roots -1+4i and -1-4i.

Answer 1

x2−10x+29

Answer 2

Well, if those were the roots, it would factor as: \[
(x-(-1+4i))(x-(-1-4i)) = 0
\]

Answer 3

So I say foil.

Answer 4

Can you do the rest?

Answer 5

\[
x^2 - (-1+4i)x - (-1-4i)x + (-1+4i) (-1-4i)
\]

Answer 6

is x^2-10x+29 the answer?

Answer 7

one way to do it is to remember that the quadratic with zeros of \(a\pm bi\) is
\[x^2-2ax+a^2+b^2\]

Answer 8

so no, your answer is incorrect

Answer 9

another way is to set
\[x=-1+4i\] and work backwards
add \(1\)
\[x+1=4i\]then square (carefully)\[(x+1)^2=(i)^2\\
x^2+2x+1=-16\]

Answer 10

thank you so much!