Question

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

Answer 1

A. x3 - 8x2 - 11x + 20
B. x3 - x2 + 22x + 40
C. x3 + x2 - 22x - 40
D. x3 + 8x2 + 11x - 20

Answer 2

I'll medal and fan help

Answer 3

for example, what is the root of this polynomial:
(x+5)

Answer 4

eek.. don't know. I suck that's why I'm asking for help.

Answer 5

do you know how to substitute into an equation?

Answer 6

a little.

Answer 7

a thrid order Polynomial can be written as:
\[y = (x-a)(x-b)(x-c)\]
where a, b and c are the roots of the polynomial. Have you ever seen it?

Answer 8

ok...the factor theorem uses substitution. It basically says... is a is a root then
f(a) = 0

Answer 9

I also put all the equations into mathway.. and they all didn't have the same roots.. maybe I typed one wrong.. idk

Answer 10

?

Answer 11

If you have an equation f(x) and suppose "a" is a root of this function, then f(a) = 0
That is, x=a will make function f(x) be zero

Answer 12

you want to find a polymonial that have three root, -5,-4 and 1

Answer 13

If we have three root, we must find a third order polynomial, since the order of the polynomial defines the number of root it have

Answer 14

So, we need to find f(x) such that f(-5) = f(-4) = f(1) = 0

Answer 15

From polynomial theory, we can write a polynomial like that:
\[y = (x-a)(x-b)(x-c)\] where a,b and c are the roots

Answer 16

Fine so far?

Answer 17

Getting the hang out it

Answer 18

now just plug the roots you have in the equation form:
\[y = (x-(-5))(x-(-4))(x-1)\]\[y = (x+5)(x+4)(x-1)\]

Answer 19

what would I do with it after

Answer 20

make the distribution of factors