Answer:
Answer:
x^{3} +3x^{2} -4x -12 =0x3+3x2−4x−12=0
Roots
To find the polynomial equation, let us transform the roots - -3, -2, and 2 - into mathematical expressions.
Let xx be the variable for roots.
(a) -3 Transpose -3 to the other side of the equation.
\begin{gathered}x = -3\\x + 3 = 0\\\end{gathered}x=−3x+3=0 Therefore, it becomes (x + 3)(x+3) .
(b) -2
\begin{gathered}x = -2\\x + 2 = 0\\(x + 2)\end{gathered}x=−2x+2=0(x+2)
(c) 2
\begin{gathered}x = 2\\x - 2 = 0\\(x - 2)\end{gathered}x=2x−2=0(x−2)
Then, combine the expressions to form an equation.
(x+3)(x+2)(x-2)=0(x+3)(x+2)(x−2)=0
Expand the new equation.
\begin{gathered}(x+3)(x+2)(x-2)=0\\(x+3)(x^{2}+2x-2x-4)=0\\(x+3)(x^{2}-4)=0\\x^{3}+3x^{2} -4x -12 = 0\end{gathered}(x+3)(x+2)(x−2)=0(x+3)(x2+2x−2x−4)=0(x+3)(x2−4)=0x3+3x2−4x−12=0
Therefore, the polynomial equation with roots -3, -2 and 2 is x^3 + 3x^2 - 4x - 12 = 0.
