Can anyone tell me if the following answer is the answer to the question below. Have I missed anything or can I add anything?:
Cubics - What form will the equations take (factorised) if they have one root, two roots, three roots?
ANSWER-
Cubic = ax3 + bx2 + cx + d
Therefore a cubic with real coeffiecients
ax3 + bx2 + cx + d = 0
If the cubic has one real root, call it t, then factored it looks like where f and g are new constants):
a(x-t)(x^2 + fx + g) = 0
If the cubic had 3 real roots, call them t, u, and v, then it can be written as:
(x-t)(x-u)(x-v) = 0.
If the cubic had 3 real roots it cannot be done because:
Any polynomial with real coefficients with nonreal roots has an even number of nonreal roots.
2007-03-27
00:02:54
·
2 answers
·
asked by
Maxim Tommani
1
in
Mathematics