Find a cubic function with the given zeros.
-2, 5, -6
help me please
x1 = - 2
x2 = 5
x3 = - 6
y = ( x - x1 ) ( x - x2 ) (x - x3 )
y = [ x - ( - 2 ) ] ( x - 5 ) [ x - ( - 6 ) ]
y = ( x + 2 ) ( x - 5 ) ( x + 6 )
y = x ^ 3 + 3 x ^ 2 - 28 x - 60
To find a cubic function with the given zeros (-2, 5, -6), we can set up equations using the zero-product property. The zero-product property states that if a polynomial function has a zero at a certain value, then the polynomial can be factored as (x - zero).
For the given zeros (-2, 5, -6), we can write the factors as follows:
(x + 2), (x - 5), and (x + 6)
Now, multiply these factors together to obtain the cubic function:
f(x) = (x + 2)(x - 5)(x + 6)
Expanding this out, we get:
f(x) = (x + 2)(x - 5)(x + 6)
= (x^2 + 2x - 5x - 10)(x + 6)
= (x^2 - 3x - 10)(x + 6)
= x^3 + 6x^2 - 3x^2 -18x - 10x - 60
= x^3 + 3x^2 - 28x - 60
Therefore, the cubic function with the zeros -2, 5, and -6 is f(x) = x^3 + 3x^2 - 28x - 60.