The Function is:
F(X) = X³ - 9X² + 20X -12
One of the roots is given, when in the statement it was said that X-6, so the root its +6......
Dividing the function by X - 6, we get the other 2 roots, because the function is composed by the multiplication of the roots in the form:
F(X) = aX³ + bX² + cX - d
(X - P).(X - Q).(X - R) (where P, Q and R are the roots)
In this problem we already have X - 6, SO
(X - P).(X - Q).(X - 6)
(X³ - 9X² + 20X -12) ÷ (X - 6) = (X - P).(X - Q)
(X³ - 9X² + 20X -12) ÷ (X - 6) = X² - 3X + 2
X² - 3X + 2
Δ = 1
X' = 2 and X'' = 1
(X - P).(X - Q).(X - 6) ⇔ (X - 2).(X - 1).(X - 6)
So
(X³ - 9X² + 20X -12) = (X - 2).(X - 1).(X - 6)
The roots are: 2, 1 and 6.... these are the points that the function crosses the x axis
F(X) = aX³ + bX² + cX - d
d = point where the function crosses the y axis
So 12 y-intercept of the graph of f(x)
