# How do you find the cubic polynomial function with two of its zeros 2 and -3+√2 and a y-intercept of 7?

##### 1 Answer

May 31, 2016

#### Explanation:

If the cubic has rational coefficients, then its other zero must be the conjugate

#f(x) = a(x-2)(x+3-sqrt(2))(x+3+sqrt(2))#

#=a(x-2)((x+3)^2-2)#

#=a(x-2)(x^2+6x+7)#

#=a(x^3+4x^2-5x-14)#

#=ax^3+4ax^2-5ax-14a#

In order that the

#f(0) = -14a=7#

So

#f(x) = -1/2x^3-2x^2+5/2x+7#

graph{-1/2x^3-2x^2+5/2x+7 [-20.34, 19.66, -9.08, 10.92]}

Note that if we do not require