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

x^3 – 3x^2 – 5x + 15

x^3 + 2x^2 – 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

 x^3 – 3x^2 – 5x + 15

 x^3 + 2x^2 – 3x – 6

 x^3 + 3x^2 – 5x – 15

solomonzelman · Answer

$$roots:~~±\sqrt{3},~2$$

Have you tried to solve the problem? I would like to see your work on this.

solomonzelman · Answer

-2, not just 2... anyway, .. what have you attempted ?

anonymous · Answer

I gave the options but I need this explained to me, sorry. Do you know how to walk me through it ?

anonymous · Answer

Or i mean can you ?

solomonzelman · Answer

The first step would be to says
$$f(x)=(x^2-3)(x+2)$$because $$x^2-3=0$$ gives that $$x= ±\sqrt{3}$$the 2 of our roots.

then
$$x+2=0$$gives    x = -2

So therefore we say that the function is
$$f(x)=(x^2+3)(x+2)$$You just need to finish this, by expending the right hand side.

Sorry for not helping -:(

anonymous · Answer

Oh! Nevermind, I figured it out! Thanks, though! (put the numbers in place and see what equation equates to zero!)