Question

a) Determine an equation, in simplified form, for the family of cubic functions with zeros 2 +- sqrt5 and 0.
b) Determine an equation for the member of the family with graph passing through point (2,20)

Answer 1

Since you have given me 4 distinct roots, the equation must be a quartic not a cubic
it would be

y = ax(x-2)(x+√5)(x-√5)
= ax(x-2)(x^2 - 5)

to find a, sub in your given point (2,20)

Answer 2

thank you again!

Answer 3

If you mean roots of 0,2+√5 and 2-√5, then then

y = x^3 - 4x^2 - x