Asked this question before but asked incorrectly.

Mar 2019
5
0
Canada
Just need assurance if i'm correct or not.

"Find the cubic equation that has zeros at -8, -4, and 13 if f(-10)=-138"

this is what i did but i think i'm not right. Can someone help correct it?
also i can keep it in standard form if correct right?
 

HallsofIvy

MHF Helper
Apr 2005
20,249
7,909
The wording of the problem seems off to me! "Find the cubic equation that has zeros at -8, -4, and 13 if f(-10)=-138" Where in the world did "f" come from? The problem is to find an equation, not a function! There is no "f"! The wording should be "Find the equation, of the form f(x)= 0, that has zeros at -8, -4, and 13 if f(-10)=-138".

It certainly is true that a cubic equation that has zeroes at x= -8, x= -4, and x= 13 must be of the form
a(x+ 8)(x+ 4)(x- 13)= 0.

I see nothing In this problem that asks us to multiply that out! Instead, since this is "f(x)= 0" and we must have f(-10)= -138, write f(-10)= a(-10+ 8)(-10+ 4)(-10- 13)= a(-2)(-6)(-23)= -276a= -138 so a= 138/276= 1/2.

The problem asked for an equation not a function so my answer would be
(1/2)(x+ 8)(x+ 4)(x- 13)= 0.