Question

how can i solve and find the polynomial f(x) that has the roots of –2, 5 of multiplicity 2. Explain how you would verify the zeros of f(x)

Answer 1

write it up in factored form

Answer 2

-2 5 5

(-2+2)(5-5)(5-5) = 0

(x+2)(x-5)(x-5) = 0

Answer 3

\[(x-2)(x+5)^{2}\]

Answer 4

close, they give you the xs; and say undo it

Answer 5

-2-2 not= 0

Answer 6

5+5 not= 0

Answer 7

so it would be (x-2)(2x-10x+25) ?

Answer 8

not quite

Answer 9

x-2 is STILL wrong

Answer 10

x+2

Answer 11

and ill assume 2x meant x^2 :)

Answer 12

yeah lol

Answer 13

(x+2)(x^2-10x+25)

good, now keep going :)

Answer 14

\[x ^{3}-8x ^{2}+5x+50\] ?

Answer 15

x^3-10x^2+25x
2x^2-20x+50
--------------------
yep, you got it

Answer 16

so how would i verify the zeros?

Answer 17

plug in the roots and see if you get zeros back :)

Answer 18

synth it if you want

Answer 19

how would i set that up?

Answer 20

the confusing way apparently lol

Answer 21

just like last question, pull the coeffs and synth it