Question

Find the polynomial equation of least degree with roots -3, 0, and 3

Answer 1

Is this Pre-Calculus?

Answer 2

yes @KingThunder314

Answer 3

The polynomial equation of least degree with roots \(\large\color{slate}{ \color{red}{a}, \color{green}{b}, \color{blue}{c} }\)

would be written as:
\(\large\color{slate}{ f(x)=(x-\color{red}{a})(x-\color{green}{b})(x-\color{blue}{c})}\)

Answer 4

so the answer would be x^3+x^2+3x-9=0? @SolomonZelman

Answer 5

For example,

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
roots \(\large\color{slate}{ \color{red}{4}, \color{green}{-3}, \color{blue}{5} }\)

polynomial of least degree
\(\large\color{slate}{ f(x)=(x-\color{red}{4})(x+\color{green}{3})(x-\color{blue}{5})}\)

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
roots \(\large\color{slate}{ \color{red}{-2}, \color{green}{6}, \color{blue}{-10} }\)

polynomial of least degree
\(\large\color{slate}{ f(x)=(x+\color{red}{2})(x-\color{green}{6})(x+\color{blue}{10})}\)

Answer 6

let me check

Answer 7

nope, it is incorrect.

Answer 8

Was I close?

Answer 9

@SolomonZelman

Answer 10

can you first write the f(x) in a similar to mine, form?

Answer 11

f(x)=(x+3)(x-0)(x-3) @SolomonZelman

Answer 12

yes that is right

Answer 13

(x-0) is same as x, correct?

Answer 14

yes

Answer 15

\(\large\color{slate}{ f(x)=x(x-3)(x+3) }\)

Answer 16

Then FOIL?

Answer 17

Lets focus on the \(\large\color{slate}{ (x-3)(x+3) }\) part for now.

The difference of squares rule: \(\large\color{slate}{ (a-b)(a+b)=a^2-b^2 }\)

Apply the difference of squares to the: \(\large\color{slate}{ (x-3)(x+3) }\) .

Answer 18

\(\large\color{slate}{ (x-3)(x+3) }\) becomes?

Answer 19

x^3-9x=0 would be the right answer right?

Answer 20

yes

Answer 21

the function would be: \(\large\color{slate}{ f(x)=x^3-9x }\)
just the polynomial is: \(\large\color{slate}{ x^3-9x }\)
(it is all same, but in different form)

Answer 22

You are very smart that you grabbed it....:)

Answer 23

Thank you for the help! @SolomonZelman

Answer 24

Sure, yw!