Write a polynomial function with single....

Question

Write a polynomial function with single zeros at -2 and 4, a double zero at 1, and a y-intercept of 24

Answer 1

 

Hi,

 

As -2, 4, and 1 are zeros of the polynomial,

 

it has (x-(-2)), (x-4), and (x-1)² as factors.

 

As 1 is a double zero,

 

the corresponding factor (x-1) has been raised to the 2nd power.

 

So, the polynomial has the form of

 

     y = a(x+2)(x-4)(x-1)²

 

As the polynomial pass therough the point (0, 24),

 

if we plug the point into the polynomial functions

 

     24 = a(0+2)(0-4)(0-1)²

 

we get a = -3.

 

So the final answer is

 

     y = -3(x+2)(x-4)(x-1)²

 

 

 

Answer 2

Hi Miguel,

 

The polynomial function will be of the following form:

 

f(x) = A(x+2)(x-4)(x-1)²   (the exponent on the (x-1) ensures multiplicity 2.

 

Since we want y-intercept to be 24, that means when x=0, y=24. That information will help us determine A.

 

24 = A (-8)

A = -3

 

So, f(x) = -3(x+2)(x-4)(x-1)² --you can choose to multiply all the factors together to get a 4th degree polynomial function written in descending order.