Solve the following equation in the complex number system

Question

x^4+x^3+4x^2+10x-60=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 x-2 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?

Answer 1

Do what Reiny said, step by step

****__x^3__+3x^2__+10x__+30________
x-2 | 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.

Answer 2

Find X such that the point(x,9) is 10 units from (9,3)