Finding the zeros of each function, and stating the multiplicity of multiple zeros?

A "zero" is a value of x that makes y = 0

y = 3x^3 - 3x

y = 3(x^3 - x)

y = 3x(x^2 - 1)

difference of squares

y = 3x(x-1)(x+1)

y will be equal to zero is any one of the three factors is zero:

if x = 0

if x = +1

if x = -1

There are no multiple zero

(if we had had a x^2 = 0 in there, then x=0 would have had multiplicity 2)

1. To find the zeros of a function just set equal to 0.

2. Since 3x is in common with 3x^3 and with 3x, you can factor it out

3. Separate and Set both factors equal to 0

4. factor out the (x^2-1) using difference of two squares separate each factor again and set equal to 0.

5. Solve for x.

6. All multiplicity of zeros is, is how many times THE SAME zero occurs. There are no multiple zeros in this problem therefore there is no multiplicity.

1. 0= 3x^3 - 3x

2. 0= 3x (x^2-1)

3. 3x=0 and x^2-1=0

4. x=0 and x+1=0 and x-1=0

5. x=0, x=-1, x=1

6. no multiplicity of zeros.

Hope this helped!

with the intention to locate zeroes, set the equation equivalent to 0 (make y=0). you are going to be able to desire to have: 0=(x+3)^3 one million: dice root the two factors 0=x+3 2: subtract 3 from the two factors -3=x -3 occurs three times. you comprehend this with the aid of fact the degree of the equation is 3. The degree of an equation is often the multiplicity. by utilising the way, the degree is the optimal means of an equation. wish this helped!

your zeros are -1,0, and 1

you can find them by guessing and checking, or by graphing the equation.

-1 because -1 cubed is still -1, times 3 gives you -3, then - 3(-1), which gives you 0

0 because anything times 0 is 0 and each term includes an x.

1 because 3 times 1 - 3 times 1 equals 0