Determine an equation of a polynomial function with zeros at X= 2, -2, 1 and y-intercept of 24

thanks in advanced! :)

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- Apr 5th 2013, 11:17 AMmarrzbarrzAdvanced Functions help... Determine an equation....
Determine an equation of a polynomial function with zeros at X= 2, -2, 1 and y-intercept of 24

thanks in advanced! :) - Apr 5th 2013, 12:13 PMMrdavid445Re: Advanced Functions help... Determine an equation....
If your zeros are 2, -2, and 1, your polynomial can be written as y=(x-2)(x+2)(x-1)-a

Since the y-intercept is 24, then 24=(0-2)(0+2)(0-1)-a

So 24=4-a, and so a=-20

Your polynomial would be y=(x-2)(x+2)(x-1)-20, and just expand the (x-2)(x+2)(x-1) part to get your final polynomial. - Apr 5th 2013, 12:47 PMPlatoRe: Advanced Functions help... Determine an equation....

Actually that does not work. Look at this.

This works: $\displaystyle -6(x-2)(x+2)(x+1)$ - Apr 5th 2013, 12:52 PMMINOANMANRe: Advanced Functions help... Determine an equation....
Hey MARZ.......

THE SOLUTION DISCRIBED BY MRDAVID IS TOTALY WRONGGGGGGGGGGGGGGGGGGGGGGGGG !!!

THE SOLUTION HE SUGGESTS (X-1)(X-2)(X+2)-20 GIVES A POLYNOMIAL X^3-X^2-4X-16....WHICH IS FAR FROM THE CORRECT ANSWER...

THE MODERATORS OF THIS FORUM MUST CHECK THE ANSWERS FROM TIME TO TIME TO AVOID SUCH FALACIES....

CORRECT SOLUTION:

CONSTRUCT A POLYNOMIAL function OF 3RD DEGREE : f(x)= ax^3+bx^2+cx+d

then f(0) = 24

f(1) =0

f(-2)=f(2) =0

solve a system of 4 simultaneous equations to find the correct answer which is

f(x) = 6x^3-6x^2-24x+24

MINOAS