62.5k views
4 votes
Find a polynomial function with the zeros ​-3,2,5 whose graph passes through the point (7,200) .

User Silex
by
8.9k points

1 Answer

3 votes

Final answer:

To find a polynomial function with the given zeros and passes through a given point, we can use the fact that the zeros of a polynomial are the values of x where the graph of the polynomial crosses the x-axis.

Step-by-step explanation:

To find a polynomial function with the given zeros and passing through a given point, we can start by using the fact that the zeros of a polynomial are the values of x where the graph of the polynomial crosses the x-axis.

So, if we have zeros at -3, 2, and 5, we can write the equation as:

(x + 3)(x - 2)(x - 5) = 0

Now, we can expand this equation and multiply the binomials:

(x + 3)(x - 2)(x - 5) = 0

x³ - 4x² - 7x + 30 = 0

So, the polynomial function is f(x) = x³ - 4x² - 7x + 30. To check if the graph passes through the point (7, 200), we can substitute x = 7 into the equation:

f(7) = 7³ - 4(7)² - 7(7) + 30 = 200

Therefore, the graph of the polynomial function passes through the point (7, 200).

User Cbyte
by
8.5k points

No related questions found

Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.