Problem 6_1
GeoGebra Construction:
6_1
Construct a cubic polynomial with integer coefficients, one of whose
roots is −3, and a second one is −1/2(1 +√−23).
Solution:
The polynomial will be divisible by (x+3), since -3 is a root. The second root is not a real root- . There is a quadratic polynomial that will be multiplied to (x+3), which will give us the cubic polynomial. We can use the quadratic formula to determine the third root. -> . Which means a=1, b=1, and c=1. Thus, the quadratic polynomial is