How to determine an equation of a polynomial function with zeros at x=2,-2,1 and y-intercept of 24?

Armani Vang

Armani Vang

Answered question

2023-01-31

How to determine an equation of a polynomial function with zeros at x=2,-2,1 and y-intercept of 24?

Answer & Explanation

Rebekah Ellison

Rebekah Ellison

Beginner2023-02-01Added 5 answers

If { 2 , - 2 , 1 } are all zeros of the polynomial
then
The factors must be present in the polynomial.
XXX ( x - 2 ) ( x + 2 ) ( x - 1 )
So
XXX y = ( x - 2 ) ( x + 2 ) ( x - 1 ) × a for some additional factor a
y ¯ = ( x - 2 ) ( x + 2 ) ( x - 1 ) = x 3 - x 2 - 4 x + 4
which is equal to 4 when x = 0
So if y = y ¯ × a is to be equal to 24 when x = 0
then a must have the value 6 when x = 0
The most obvious value for a is, however,
XXX ( x + 6 )
in which case
XXX y = ( x - 2 ) ( x + 2 ) ( x - 1 ) ( x + 6 )
XXXX = x 4 + 5 x 3 - 10 x 2 - 20 x + 24

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