Question

What is the third–degree polynomial function such that f(0) = –24 and whose zeros are 1, 2, and 3?

Answer 1

start with
\[f(x)=a(x-1)(x-2)(x-3)\]

Answer 2

then solve for \(a\) via
\[f(0)=a(-1)(-2)(-3)=-24\]

Answer 3

So it'll be f(x) = 2x3 – 24x2 + 22x – 24 ?

Answer 4

i think \(a=4\) right?

Answer 5

\(-6a=-24\iff a=4\)

Answer 6

4x^3 then?

Answer 7

so it is whatever you get when you multiply
\[f(x)=4(x-1)(x-2)(x-3)\]

Answer 8

f(x) = 4x3 – 24x2 + 44x – 24?

Answer 9

\[4 x^3-24 x^2+44 x-24\]

Answer 10

yeah, that one

Answer 11

Thank you so much

Answer 12

yw