College Algebra
posted by Jennifer on .
Solve the following equation in the complex number system
x^4+x^3+4x^2+10x60=0
College Algebra  Reiny, Monday, January 2, 2012 at 11:49pm
hint
x = 2 and x = 3 are roots
so either do long division by x2 and x+3
to get a quadratic or do it by synthetic division.
Solve that quadratic using the formula.
College Algebra  Jennifer, Tuesday, January 3, 2012 at 8:10pm
so what would my equation be to figure this question out?

Do what Reiny said, step by step
****__x^3__+3x^2__+10x__+30________
x2  x^4 + x^3 + 4 x^2 + 10 x  60
******x^4 2x^3
******
**********3 x^3 + 4 x^2 + 10 x  60
**********3 x^3  6 x^2
**********
****************+10 x^2 + 10 x 60
****************+10 x^2  20 x
******************
*************************+30 x 60
*************************+30 x 60
*************************
Remainder = 0
Now divide x^3+3x^2+10x+30
by x + 3
That will leave you with a quadratic which you solve with the quadratic equation, probably resulting in two complex conjugate roots. 
Find X such that the point(x,9) is 10 units from (9,3)