Answer: [tex]6x^{3}+19x^{2} +3x=0[/tex]
Step-by-step explanation:
The formula to calculate the equation of the polynomial is given by :
[tex](x-\alpha )(x-\beta )(x-v) = 0[/tex]
where : [tex]\alpha ,\beta[/tex] and [tex]v[/tex] are the zeros , that is , the roots of the equation.
substituting the zeros into the equation , we have :
[tex](x-0)(x-(-\frac{1}{6}))(x-(-3) =0[/tex]
⇒ [tex]x(x+\frac{1}{6})(x+3)=0[/tex]
expanding , we have
[tex](x^{2} +\frac{x}{6})(x+3) = 0[/tex]
⇒[tex]x^{3}+3x^{2} +\frac{x^{2}}{6}+\frac{3x}{6}=0[/tex]
multiplying through by 6 , we have
[tex]6x^{3}+18x^{2} +x^{2} +3x=0[/tex]
⇒[tex]6x^{3}+19x^{2} +3x=0[/tex]
therefore , the equation P is [tex]6x^{3}+19x^{2} +3x=0[/tex]
