Question

write a polynomial function with rational coefficients in standard for whose zeros are x= -3,-4,2

Answer 1

A polynomial function (with rational coefficients) with zeros: \(\large\color{black}{ \color{red}{a},~\color{green}{b},~\color{blue}{c} }\) is:

\(\large\color{black}{ f(x)=(x- \color{red}{a})(x-\color{green}{b})(x-\color{blue}{c} }\))

Answer 2

Do you want an example?

Answer 3

so just plug in the numbers

Answer 4

Yes, basically, your \(\large\color{black}{ \color{red}{a}}\) is \(\large\color{black}{ \color{red}{-3}, }\) your \(\large\color{black}{ \color{green}{b} }\) is \(\large\color{black}{ \color{green}{-4}, }\) and your \(\large\color{black}{ \color{blue}{c} }\) is \(\large\color{black}{ \color{blue}{2} . }\)

Answer 5

After you plug in your numbers, you would then have to expand your function (I think).

Answer 6

do u have the answer

Answer 7

is it 24

Answer 8

you are writing a function.... I don't see how would you get 24.

Answer 9

Ok so u get f(x) = (x+3) (x+4) (x-1)

Answer 10

you mean (x-2) at the end?

Answer 11

well yes

Answer 12

Good now you have to expand this, since you are asked to write a function with rational coefficients.

Answer 13

how

Answer 14

oh ya

Answer 15

I made a mistake.

Answer 16

it is...
\(\large\color{black}{ f(x)=(x+ 3)(x+4)(x-2 }\))

Answer 17

So, you have to first start from expanding, \(\large\color{black}{ (x+ 3)(x+4) }\)

Answer 18

ok i got tht

Answer 19

sure, can you tell me what you got then, please?

Answer 20

alright x squared + 7x +12

Answer 21

yes, that is correct:
So now instead of having, \(\large\color{black}{ f(x)=(x+ 3)(x+4)(x-2 ) }\)

you have: \(\large\color{black}{ f(x)=(x^2+7x+12)(x-2 ) }\)

Answer 22

you have to expand the last time and you are done.

Answer 23

if you have a question regarding how to do it, please ask.

Answer 24

ok i got x cubed + 5x squared -2x -24

Answer 25

yes, that's right again: this is your function: \(\large\color{black}{f(x)=x^3+5x^2-2x-24 }\)
(and just as asked, with rational coefficients....)

Answer 26

Any more questions about the problem?

Answer 27

btw, you can use my code: `\(\large\color{black}{ f(x)=x^3+5x^2-2x-24 }\)`

Answer 28

no im good on tht one thank you but i have another

Answer 29

yw;)

Answer 30

\[^{3}\sqrt{a ^{16}}b ^{19}\]
how to simplify

Answer 31

anyone here

Answer 32

\(\Large\color{black}{ \sqrt[3]{a^{16}b^{10}} }\)
(made a size larger, `\(\Large\color{black}{ \sqrt[3]{a^{16}b^{10}} }\)` )

anyway, lets break it down like this:

\(\Large\color{black}{ \sqrt[3]{a^{15}\times a\times b^{9}\times b} }\)

Answer 33

alright then wut

Answer 34

I lost my latex, got disconnected.

Answer 35

ohh i thought you left me

Answer 36

oh man, again~ I'll draw it, okay?

Answer 37

alright