I just wanted to double check that I am correct.
1.Find the zeros for the function:
f(x)= 4(x-3)(x+2)(x-4)^2
Zeros are: 3,-2, 4(multiplicity 2)
2.Find the zeros for the function:
f(x)= x^3-9x
Zeros are: 0, 3, -3
both correct
Yes, you are correct!
To find the zeros of a function, you need to set the function equal to zero and solve for x.
Let's go through each question step by step:
1. Find the zeros for the function f(x) = 4(x-3)(x+2)(x-4)^2:
To find the zeros, we set f(x) equal to zero:
4(x-3)(x+2)(x-4)^2 = 0
Now, we can see that the function will be equal to zero if any of the factors are equal to zero. So, we set each factor equal to zero and solve for x:
x-3 = 0 --> x = 3
x+2 = 0 --> x = -2
(x-4)^2 = 0 --> x - 4 = 0 --> x = 4
So, the zeros of the function are x = 3, x = -2, and x = 4 (with multiplicity 2).
2. Find the zeros for the function f(x) = x^3-9x:
Again, we set f(x) equal to zero:
x^3-9x = 0
This equation is a cubic equation, and there are various methods to solve it. However, in this case, we can factor out the common factor of x:
x(x^2-9) = 0
Now, we set each factor equal to zero and solve for x:
x = 0
Next, x^2-9 = 0. This equation is a difference of squares, so we can factor it:
(x+3)(x-3) = 0
Setting each factor equal to zero, we get:
x + 3 = 0 --> x = -3
x - 3 = 0 --> x = 3
So, the zeros of the function are x = 0, x = -3, and x = 3.
Well done! You have correctly found the zeros of the given functions.