check my answer please find the number of zeros(x-intercepts) y=3k^3-6k^2-45k=k(3k+9)(k-5)= k(3k^2-15k+9k-45)=k(3k^2-6k-45) or should i do it 3k(k-5) (k+3)=3k(k^2+3k-5k-15)=3k(k^2-2k-15) which on is the right one please let me know.thanks
Yes you factor
3k(k-5)(k+3) and your check says you did it correctly
Now to find the zeros
Set each factor = 0. And solve
3k=0. K=0
K-5=0. K=5
K+3=0. K=-3
To find the number of zeros or x-intercepts of the equation, we need to determine the factors of the equation and their corresponding values that make the equation equal to zero.
Let's start by analyzing your first version:
y = 3k^3 - 6k^2 - 45k = k(3k + 9)(k - 5) = k(3k^2 - 15k - 45)
This is a correct factoring of the equation. Now, let's analyze the factors:
k = 0: When k = 0, the equation becomes 0(3(0)^2 - 15(0) - 45) = 0. So, k = 0 is a solution, and this gives us one x-intercept.
3k + 9 = 0: Solving this equation gives k = -3. Substituting this value into the equation, we get (-3)(3(-3)^2 - 15(-3) - 45) = 0. Therefore, k = -3 is another x-intercept.
k - 5 = 0: Solving this equation gives k = 5. Substituting this value into the equation, we get (5)(3(5)^2 - 15(5) - 45) = 0. Thus, k = 5 is another x-intercept.
So, the zeros or x-intercepts of the equation are k = 0, k = -3, and k = 5.
To clarify your second version:
y = 3k(k - 5)(k + 3) = 3k(k^2 + 3k - 5k - 15) = 3k(k^2 - 2k - 15)
This is also a correct factoring of the equation. Analyzing the factors:
k = 0: When k = 0, the equation becomes 3(0)(0^2 - 2(0) - 15) = 0, giving us k = 0 as a solution and one x-intercept.
k^2 - 2k - 15 = 0: By solving this quadratic equation, we find that the zeros are k = 5 and k = -3. Substituting these values into the equation, we get 3(5)(5^2 - 2(5) - 15) = 0 and 3(-3)(-3^2 - 2(-3) - 15) = 0. Hence, k = 5 and k = -3 are additional x-intercepts.
As you can see, both versions yield the same x-intercepts: k = 0, k = -3, and k = 5. Therefore, both versions are correct, and you can choose either one to express the equation's x-intercepts.