Answer:
2
Step-by-step explanation:
We already have the zeros, so we can write the cubic polynomial in this general form:
[tex]y = a(x - x_1)(x - x_2)(x - x_3)[/tex]
Where:
[tex]x_1 = 5[/tex]
[tex]x_2 = 5i[/tex]
[tex]x_3 = -5i[/tex]
So we have that:
[tex]y = a(x -5)(x - 5i)(x + 5i)[/tex]
[tex]y = a(x -5)(x^2 + 25)[/tex]
To find the value of the leading coefficient 'a', we can use the point (1, -208) given:
[tex]-208 = a(1 -5)(1 + 25)[/tex]
[tex]-208 = a(-4)(26)[/tex]
[tex]a = -208 / (-104) = 2[/tex]
So the leading coefficient is 2.
