Question

Which of the following is a polynomial with roots

Answer 1

Which of the following is a polynomial with roots \[-\sqrt{3} \sqrt{3} -2\]

A. x^3 – 2x^2 – 3x + 6

B. x^3 + 2x^2 – 3x – 6

C. x^3 – 3x^2 – 5x + 15

D. x^3 + 3x^2 – 5x – 15

Answer 2

uhh.. help?

Answer 3

What are your roots, can you make it clear??

Answer 4

the roots are \[-\sqrt{3} \sqrt{3} -2\]

Answer 5

I mean where is the comma. You are giving only one root

Answer 6

-(sqrt)3, (sqrt)3, -2

Answer 7

Method 1 :
make the equation as

(x+(sqrt) 3)(x-(sqrt)3)(x+2)

Now open and simplify to get your equation

method 2 :.

Substitute -(sqrt)3, (sqrt)3 , -2 in each equation and see which equation gives 0 for all the 3 roots. That is your answer

Answer 8

i don't get it, if you multiply x and -(sqrt)3 what do you get?

Answer 9

You can also use the fact that if the leading coefficient is 1, then the second coefficient is the negative of the sum of the roots. So the second coefficient must be:\[(--\sqrt{3}+\sqrt{3}-2)=2\]

Answer 10

oops, meant:\[-(-\sqrt{3}+\sqrt{3}-2)=2\]

Answer 11

@Tributized , it is
\[(x+\sqrt{3})(x-\sqrt{3})(x+2)\]

Answer 12

yes you distribute x to the other x, distribute x to -(sqrt)3 then (sqrt)3 to x then (sqrt)3 to -(sqrt)3

Answer 13

So you get \[(x ^{2}-3)(x+2)\]

so you get x^3 + 2x^2 – 3x – 6

Answer 14

could you explain how you got x^2-3 and x+2?

Answer 15

See,

You mentioned the roots as -(sqrt)3, (sqrt)3, -2
So for
x= -(sqrt)3 or x+ (sqrt)3 = 0

Similarly
x= (sqrt)3 or x - (sqrt)3 = 0
x= -2 or x+2= 0

Now ( x+ (sqrt)3) ( x - (sqrt)3)(x+2)=0

I hope you got it now @Tributized

Answer 16

oh ok lol thanks

Answer 17

By using identity (a+b)(a-b)=a^2-b^2

Answer 18

( x+ (sqrt)3) ( x - (sqrt)3) = (x^2−3)

Answer 19

oh so if you multiply x to -(sqrt)3 the (sqrt) is removed and just becomes -3?

Answer 20

i get the x^2 just not the square root thingy.

Answer 21

NO bro. It is
\[(a+b)(a-b)=a ^{2}-b ^{2}\]

Here a=x b=sqrt(3) Substitute and get your answer