A cubic function y has real coefficients, and its zeros are 4, 5 and 1. If x=−3, =−448 satisfies its equation, find the equation of the cubic function in standard form.
Let the leading coefficient be a if necessary.
Please help!
We have that
y = a ( x -1) ( x - 4) ( x - 5)
And when x= -3, y = -448 so we have
-448 = a ( -3 -1) ( -3 - 4) ( -3 - 5)
-448 = a ( -4) (-7) (-8)
-448 = a ( -224)
a = -448/ -224 = 2
So the polynomial is
y = 2 ( x - 1) ( x - 4) (x - 5)
y = 2 ( x^2 - 5x + 4) ( x -5)
y = 2 ( x^3 - 5x^2 + 4x - 5x^2 + 25x - 20)
y = 2 ( x^3 - 10x^2 + 29x -20)
y = 2x^3 - 20 x^2 + 58x - 40