Question

What polynomial has roots of –5, –4, and 1 ?

Answer 1

(x + 5)(x + 4)(x - 1) = 0

Zero product property. Multiply out if you can't use this form.

Answer 2

Roots means solutions so that means that each of these were factors

bluepig is correct in the setup

Answer 3

x3 – 8x2 – 11x + 20

x3 – x2 + 22x + 40

x3 + x2 – 22x – 40

x3 + 8x2 + 11x – 20

Answer 4

ya I m with blupig u can do it

Answer 5

nah I really can't but ok

Answer 6

@ornadios did you understand?

Answer 7

no

Answer 8

you can also plug your answers in and see if they give you zero, since they would have to be solutions to the correct answer.

Answer 9

We are given that the roots are -5. -4 and 1
so the factors of the polynomial are (x+5), (x+4) and (x-1)
@ornadios Do you understand this?

Answer 10

if x is root and x=5 is answer then x-5 is a factor of that polynomial according to remainder theorem .did u understand.

Answer 11

Yeah I think I got what ashely was saying

Answer 12

@ornadios now to find the polynomial we need to find the product of these factors
\[(x+5)(x+4)(x-1)\]Can you find the product @ornadios?

Answer 13

ya u can do it!go

Answer 14

ok one sec

Answer 15

I'm here, let me know if you get stuck anywhere

Answer 16

x3 – 8x2 – 11x + 20 answer

Answer 17

I think the general polynomial is \[(x+5)^m (x+4)^n (x-1)^k\]

Answer 18

@ornadios check again, you should get
\[x^3+8x^2+11x-20\]

Answer 19

@anhkhoavo1210 Multiples of it as well.

Answer 20

thank you it was one of the questions on my semester exam and I honestly did not know how to do it it thank you. Need this class to graduate on time :)

Answer 21

@ornadios you're welcome:)