Posted by **madi** on Wednesday, January 19, 2011 at 6:37pm.

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

- algebra 2 -
**Reiny**, Wednesday, January 19, 2011 at 7:47pm
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:

**x^2 - 8x + 7 = 0**

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.

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