Determine an equation of a polynomial function with zeros at X= 2, -2, 1 and y-intercept of 24
thanks in advanced!
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.
Actually that does not work. Look at this.
This works: $\displaystyle -6(x-2)(x+2)(x+1)$
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