the polynomial equation $x^{3}+x^{2}=-9x - 9$ has complex roots $pm3i$. what is the other root? use a…

the polynomial equation $x^{3}+x^{2}=-9x - 9$ has complex roots $pm3i$. what is the other root? use a graphing calculator and a system of equations.\n-9\n-1\n0\n1

the polynomial equation $x^{3}+x^{2}=-9x - 9$ has complex roots $pm3i$. what is the other root? use a graphing calculator and a system of equations.\n-9\n-1\n0\n1

Answer

Explanation:

Step1: Rewrite the equation

First, rewrite the polynomial equation $x^{3}+x^{2}=-9x - 9$ in standard form $x^{3}+x^{2}+9x + 9 = 0$.

Step2: Factor by grouping

Group the terms: $(x^{3}+x^{2})+(9x + 9)=0$. Factor out the common factors from each group: $x^{2}(x + 1)+9(x + 1)=0$. Then, factor out $(x + 1)$ to get $(x + 1)(x^{2}+9)=0$.

Step3: Solve for x

Set each factor equal to zero. For $x^{2}+9 = 0$, we have $x^{2}=-9$, so $x=\pm3i$. For $x + 1=0$, we get $x=-1$.

Answer:

-1