Write the simplest polynomial function with zeros five and -4.
K(x) = x^2 - x - 20?
To find the simplest polynomial function with zeros at five and -4, you can use the zero product property. This property states that if a polynomial has a zero at a certain value, then the polynomial can be factored with x - a as one of its factors, where a is the zero value.
So, we can start by using the values of the zeros, five and -4, to create the factors:
(x - 5) and (x + 4).
To find the simplest polynomial function, we multiply these factors together:
(x - 5)(x + 4)
Expanding the expression, we have:
x(x + 4) - 5(x + 4)
Multiplying each term, we get:
x^2 + 4x - 5x - 20
Simplifying, we have the simplest polynomial function with zeros at five and -4:
K(x) = x^2 - x - 20.