Which of the following is a polynomial with roots – square root of 3, square root of 3, and –2 ?

x^3 – 2x^2 – 3x + 6

x3 – 3x^2 – 5x + 15

x^3 + 2x2 – 3x – 6

x^3 + 3x^2 – 5x – 15

Question

Which of the following is a polynomial with roots – square root of 3, square root of 3, and –2 ?

x^3 – 2x^2 – 3x + 6

x3 – 3x^2 – 5x + 15

x^3 + 2x2 – 3x – 6

x^3 + 3x^2 – 5x – 15

anonymous · Answer

You can do this 2 ways. Do you have any idea how?

anonymous · Answer

$$-\sqrt{3},  \sqrt{3} and -2$$

anonymous · Answer

Not really andras

anonymous · Answer

You can check each individually but this would take forever. (some time)
Or you are wise and know that if a polynomial has three roots: lets say a,b,c than its equation is
(x-a)(x-b)(x-c)
Do you see how this can help you?

anonymous · Answer

No

anonymous · Answer

I don't see the a b and c values :l

anonymous · Answer

$$(x--\sqrt{3})(x-\sqrt{3})(x--2)=solution $$

anonymous · Answer

ok so whats our first step?

anonymous · Answer

This was the first step. 
The second step is the expand those brackets!

anonymous · Answer

As the solutions are given it is easy to see that it can only be
x^3 + 2x^2 – 3x – 6
I only taken a look at -6.
The only part of this polynomial without x is the:
$$(--\sqrt{3})(-\sqrt{3})(--2)=-6$$

anonymous · Answer

Thanks man :)