Answer:
x = 3 , -1 + [tex]\sqrt{-1}[/tex] , -1 - [tex]\sqrt{-1}[/tex]
Step-by-step explanation:
⇒ [tex]p(x)=x^{3} -x^{2} -4x-6[/tex]
⇒ [tex]p(x)=(x-3)(x^{2} +2x+2)[/tex]
now, for zeros of [tex](x^{2} +2x+2)[/tex],
⇒ x = [tex]\frac{-b}{2a}[/tex] ± [tex]\frac{\sqrt{b^{2}-4ac } }{2a}[/tex]
⇒ x = [tex]\frac{-2}{2}[/tex] ± [tex]\frac{\sqrt{2^{2}-4(2) } }{2}[/tex]
⇒ x = -1 ± [tex]\sqrt{-1}[/tex]
hence, all the roots are,
x = 3, -1 + [tex]\sqrt{-1}[/tex], -1 - [tex]\sqrt{-1}[/tex]
