How do I determine the equation of a quartic function with complex roots 3 + 2i and 2 - 3i
2006-09-11 14:24:15 · 5 answers · asked by kira 2 in Science & Mathematics ➔ Mathematics
To determine the equation of a quartic function with complex roots, you have to first know that complex roots come in conjugates. Eg if you have 3+2i, you also are forced to have a root of 3-2i.
To find your equation, you can take all your roots and put them into an equation of the form
(x-(3+2i))(x-(3-2i)(x-(2-3i))(x-(2+3i))
and expand to get your quartic equation:
x^4-10x^3+50x^2-130x+169
2006-09-11 14:33:17 · answer #1 · answered by priestlake22 2 · 0⤊ 0⤋
A quadratic equation ax^2+bx+c=0 with complex roots will have all real coefficients (a, b and c) if the roots are conjugates. Since the given roots are not conjugates, the equation will not have all real coefficients.
The equation is
x^2 - (3+2i+2-3i)x+(3+2i)(2-3i)=0
x^2-(5-i)x +(12-5i)=0
2006-09-12 04:39:07 · answer #2 · answered by Amit K 2 · 0⤊ 0⤋
The equation is (x-(3+2i))(x-(2-3i))=0 or x^2-(5-i)x+12-5i=0
2006-09-11 21:29:44 · answer #3 · answered by karlterzaghi 2 · 0⤊ 0⤋
go to walmart and buy a TI-89... put it in there and you are done..
2006-09-11 21:28:49 · answer #4 · answered by ThisGalRocks! 3 · 0⤊ 0⤋
is this ur homework?
2006-09-11 21:26:52 · answer #5 · answered by Gabriela 2 · 0⤊ 0⤋