Posted by kaitlyn on Saturday, April 10, 2010 at 3:38pm.
what are the other roots of 3x^4-12x^3+41x-8x+26 that include 2-3i
algerbra 2 - Damon, Saturday, April 10, 2010 at 4:11pm
Assume you mean:
Well then 2+3i must be one
(x -2+3i)(x - 2-3i) = x^2 -4x +13
divide by that and get
so the other two roots are
x=sqrt(2/3) and x = -2/3
algerbra 2 - Reiny, Saturday, April 10, 2010 at 4:16pm
First of all, I will assume you have a typo and the third term should be 41x^2
complex roots always come in conjugate pairs, that is,
if 2-3i is a root, so is 2+3i
sum of those roots = 4
product of those roots = 3-9i^2 = 13
so the quadratic that yields those two roots is
x^2 - 4x + 13
I then did an algebraic long division by x^2 - 4x + 13 and that came out very nicely to an answer of 3x^2 + 2 with no remainder.
(x^2 - 4x + 13)(3x^2 + 2) = 0
x = 2-3i, 2+3i from the first part and
x^2 = -2/3
x = ± √-(2/3)
= ± i√(2/3) or ±(1/3)i √6
Answer This Question
More Related Questions
- algebra 2 - find all rational roots of the polynomial 6x^3-13x^2-41x-12=0
- Math - Find a polynomial of degree 3 with roots 3, 4 - i. Which one is it? A.x3...
- algebra - find a third degree polynomial equation with coefficients that has ...
- math algerbra 1 - 3(4+4x)=12x+12
- algerbra - how do you factor x2+12x+35
- math - I HAVE THESE ANSWERS FOR THE PROBLEMS. COULD YOU DOUBLE CHECK PLEASE, ...
- algerbra - If 1 and –6 are two of the roots of 6x^4 + 31 x^3 − 33x^2 ...
- Math - How to factor x^3 - 3x^2 + 4 =0 Use D'Alembert's Rational Roots Theorem. ...
- Algerbra 2 - find the possible roots for: 3x^3-6x^2+11x-6=0
- math - Could you please solve so I can double check my answers for the practice ...