Answer:
The quadratic equation is [tex]f(x) = 2x^2 + 6x + 4[/tex]
Step-by-step explanation:
Zeros of a function:
Given a polynomial f(x), this polynomial has roots [tex]x_{1}, x_{2}, x_{n}[/tex] such that it can be written as: [tex]a(x - x_{1})*(x - x_{2})*...*(x-x_n)[/tex], in which a is the leading coefficient.
Roots are -2 and -1 and the leading coefficient 2
This means that [tex]x_1 = -2, x_2 = -1, a = 2[/tex]
So
[tex]f(x) = 2(x - (-2))(x - (-1)) = 2(x + 2)(x + 1) = 2(x^2 + 2x + x + 2) = 2(x^2 + 3x + 2) = 2x^2 + 6x + 4[/tex]
The quadratic equation is [tex]f(x) = 2x^2 + 6x + 4[/tex]
