Please help me turn this into an equation.

Question

Write a polynomial f(x) of degree 3 that has the zeros 1/3, √3  and -√3 then solve

Answer 1

The problem gives the zeros (that is, the values of x for which the polynomial is 0).  The Multiplicative Property of Zero states that anything multiplied by 0 produces 0.  So, this polynomial equation is:

     (x-1/3)(x-√3)(x+√3) = 0

 

Now, if you want to represent that differently, use F-O-I-L twice to distribute and then collect like terms:

     (3x-1)(x²-3) = 0             [multiply by 3; use F-O-I-L once]

     3x³ - 9x - x² + 9 = 0          [F-O-I-L a second time]

   3x³ - x² - 9x + 9 = 0             [re-arrange terms]