Can the root of a polynomial P(x) =3x^3 - 10x^2 - 5x be equal to -2/3?

The root of a polynomial P(x) is a number that makes P(x)
equal to 0.

Now we are given P(x) = 3x^3 - 10x^2 -
5x.

If we substitute -2/3 for x in P(x), we
get

P (-2/3) = 3*(-2/3) ^3 – 10 *(-2/3) ^2 –
5*(-2/3)

= 3*(-8 / 27) – 10*(4/9) –
5*(-2/3)

= -8 / 9 – 40/9 +
20/3

= -18 / 9

=
-2

We see that -2 is not equal to
zero.

Therefore -2/3 is not a root of 3x^3 -
10x^2 - 5x.