Dtermine an equation, in simplified form, for the family of cubic functions with zeros 2 and 4+-sqrt. 3.

Answer 1

y = (x-2)(x-4-√3)(x-4+√3)
= (x-2)(x² - 8x + 13)

How did I get that quadratic? One way is to just multiply all the stuff out, the other is to realize that

4 ± √3 = (8 ± 2√3)/2 = (8 ± √12)

So, -b = 8
b² - 4ac = 64 - 4ac = 12
so, 4ac = 52 = 4*13
We have a=1, so c=13

y = (x-2)(x² - 8x + 13)
x³ - 10x² + 29x - 26