Question

what is the quadratic function that has the roots (4+3i) and (4-3i)

Answer 1

there is a fast way to do this using the property
if
ax^2 + bx + c = 0, then
sum or roots = -b/a
product of roots = c/a

sum of roots = (4+3i) + (4-3i) = 8
product of roots = (4+3i)(4-3i) = 16-9 = 7

equation:
<b>x^2 - 8x + 7 = 0</b>

another way is to form the factors:
(x - (4+3i)) and (x - (4-3i)) and set

(x - (4+3i))(x - (4-3i)) = 0
(x - 4 - 3i)(x - 4 + 3i) = 0
carefully expand, simplify and you will get the above answer.