Question

Find the zeros of polynomial functions and solve polynomial equations.
f(x)=x^3-5x^2-9x+45

Answer 1

Find the zeros, just equal the equation to 0.

x³ - 5x² - 9x + 45 = 0

Factor:

x².(x - 5) - 9.(x - 5) = 0

(x² - 9).(x - 5) = 0

It's a multiplication, so, if one term goes to 0, everything goes too.

x² - 9 = 0

x² = 9

x = + or - √9

x' = 3

x'' = -3

x - 5 = 0

x = 5

Now we have three roots: -3, 3, 5.