Question

Find the zeros of each function. State the multiplicity of multiple zeros y=2x^3+x^2-x

Answer 1

Answer:

  -1, 0, 1/2

Step-by-step explanation:

The function can be factored as ...

  y = x(2x^2 +x -1)

  y = x(2x -1)(x +1)

The factors are unique, so each zero has multiplicity 1. The zeros are the values of x that make the factors zero:

  -1, 0, 1/2 . . . . zeros of the function; each with multiplicity 1

Answer 2

Answer:

Step-by-step explanation:

To find the roots/zeros, set

2

x

3

+

x

2

−

x

equal to

0

and solve.

2

x

3

+

x

2

−

x

=

0

Factor the left side of the equation.

Tap for more steps...

x

(

2

x

−

1

)

(

x

+

1

)

=

0

If any individual factor on the left side of the equation is equal to

0

, the entire expression will be equal to

0

.

x

=

0

2

x

−

1

=

0

x

+

1

=

0

Set the first factor equal to

0

.

x

=

0

Set the next factor equal to

0

and solve.

Tap for more steps...

x

=

1

2

Set the next factor equal to

0

and solve.

Tap for more steps...

x

=

−

1

The final solution is all the values that make

x

(

2

x

−

1

)

(

x

+

1

)

=

0

true. The multiplicity of a root is the number of times the root appears.

x

=

0

(Multiplicity of

1

)

x

=

1

2

(Multiplicity of

1

)

x

=

−

1

(Multiplicity of

1

)