Question

Find all the zeroes of the equation.
x3 + x2 = –3x – 3

Answer 1

I take it that is supposed to be read as \[x^{3}+x^{2}=-3x-3\] correct?

Answer 2

Yes

Answer 3

Assuming so, move everything to one side, \[x^{3}+x^{2}+3x+3=0\] then factor in pairs. By that I mean, first factor the pair \[x^{3}+x^{2}=x^{2}(x+1)\] and then factor the pair \[3x+3=3(x+1)\] This produces the equation \[x^{2}(x+1)+3(x+1)=0\] Now each term here has x+1 in it, so we factor that out and get \[(x+1)(x^{2}+3)=0\] and so we know that either \[x+1=0\] or \[x^{2}+3=0\] If the first one is true, then x=-1 is a root. If the second one is true, then \[x^{2}=-3\] and so square-rooting both sides gives \[x=\pm i\sqrt{3}\] and so these are the roots of the equation.

Answer 4

So it would be.. D?

Answer 5

No, the first answer choice.

Answer 6

Ah! I see, Thank You!