Question

Find the zero of the polynomial X3+2x2-2x-1

Answer 1

Answer:

$x = 1 , \frac{-3+\sqrt{5} }{2} ,\frac{-3-\sqrt{5} }{2}$

Step-by-step explanation:

By verification, 1 is a root of the polynomial  $x^{3}+2x^{2}-2x-1$ .

So, by synthetic division method, we can get the other two roots.

Then we get, $(x-1)(x^{2}+3x+1)=0$

From this  $x^{2} +3x+1 =0$  => $x=\frac{-3+\sqrt{9- 4 } }{2} (or)\frac{-3-\sqrt{9-4} }{2}$

Therefore,  $x = 1 , \frac{-3+\sqrt{5} }{2} ,\frac{-3-\sqrt{5} }{2}$