what is an equation of a polynomial function that has zeros at -3 and -2?
Y = (x+3)(x+2) = 0.
x^2+2x+3x+6 = 0,
x^2 + 5x + 6 = 0.
Y = x^2 + 5x + 6.
To find an equation of a polynomial function with zeros at -3 and -2, we can use the fact that if a number a is a zero of the polynomial function, then (x - a) is a factor of the polynomial.
So, if -3 and -2 are zeros, then (x + 3) and (x + 2) are the corresponding factors.
To obtain the equation, we multiply these factors together:
(x + 3)(x + 2) = x^2 + 5x + 6
Therefore, the equation of the polynomial function with zeros at -3 and -2 is f(x) = x^2 + 5x + 6.
To find the equation of a polynomial function with given zeros, you can start by using the zero product property. This property states that if a * b = 0, then either a = 0 or b = 0. In this case, we know that the zeros are -3 and -2. So we can write two separate equations:
(x + 3) = 0
(x + 2) = 0
To find the equation, we need to multiply these factors together. When multiplying two binomials, such as (x + a) and (x + b), we typically use the FOIL method:
(x + 3)(x + 2)
= x(x) + x(2) + 3(x) + 3(2)
= x^2 + 2x + 3x + 6
= x^2 + 5x + 6
Therefore, the equation of the polynomial function with zeros at -3 and -2 is f(x) = x^2 + 5x + 6.