Question

multiply (x+1)(x−4)(x−√3) into standard polynomial form

Answer 1

I got x3−3x2−4x−x23√+3x3√+43√
but i graphed it and the zeros were not right

Answer 2

or do imaginary numbers come into play?

Answer 3

x^3+sqrt(3) x^2+5 x^2+5 sqrt(3) x+4 x+4 sqrt(3)

Answer 4

\[x ^{3}-3x ^{2}-x ^{2}\sqrt{3}+3x \sqrt{3}+4\sqrt{3}-4x\]

Answer 5

\[(x-a)(x-b)(x-c)=(x^2-bx-ax+ab)(x-c)\]
\[=x^3-cx^2-bx^2+bcx-ax^2+acx+abx-abc\]
\[=x^3-(a+b+c)x^2+(ab+ac+bc)x-abc\]

Answer 6

When I put yours in Chris the zeros came out right on the calculator. May I ask how you came to the answer you got? when i multiply the square root is where i get messed up.

Answer 7

\[a+b+c=-1+4+\sqrt{3}=3+\sqrt{3} \]
\[ab+ac+bc=-1(4)+(-1)(\sqrt{3})+4\sqrt{3}=-4-1\sqrt{3}+4\sqrt{3}=-4+\sqrt{3} \]
\[abc=-1(4)\sqrt{3}=-4\sqrt{3}\]

Answer 8

i am going to make a bet, which is that whoever gave you this problem meant "integer coefficients" not "real coefficients" and so you were not supposed to do all this. that is just a guess though

Answer 9

when you originally posted i though you should use
\[(x+1)(x-4)(x-\sqrt{3})(x+\sqrt{3})\] and that will give you integer coefficients. of course i could be wrong because it did say "real" not "integer"

Answer 10

The problem said write a polynomial function using the given zeros

Answer 11

and those were -1,4, sqt3

Answer 12

i put those in the equation i put above

Answer 13

he's wondering about the coefficients though
does it say real or integer coefficients?

Answer 14

or does it not say anything?

Answer 15

i don't have it in front of me but I'm pretty sure it did not say

Answer 16

What chris posted though worked and i got the zeros when i graphed it

Answer 17

tbh, I popped it into Wolfram alpha to get that

Answer 18

ok i have looked at your posting before this and it said find a polynomial of least degree having these zeros
it does say least degree
if so then you are correct in saying (x+1)(x-4)(x-sq3)

Answer 19

But then you are suppose to put it into polynomial form.

Answer 20

standard form?
i wrote this for you in standard form above

Answer 21

\[x^3-\sqrt{3} x^2-3 x^2+3 \sqrt{3} x-4 x+4 \sqrt{3}\] is one answer
http://www.wolframalpha.com/input/?i=%28x%2B1%29%28x-4%29%28x-sqrt%283%29%29