2007 iTest Problems/Problem 23

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Problem

Find the product of the non-real roots of the equation \[(x^2-3)^2+5(x^2-3)+6=0\]

$\text{(A) } 0\quad \text{(B) } 1\quad \text{(C) } -1\quad \text{(D) } 2\quad \text{(E) } -2\quad \text{(F) } 3\quad \text{(G) } -3\quad \text{(H) } 4\quad \text{(I) } -4\quad \$ (Error compiling LaTeX. Unknown error_msg)

$\text{(J) } 5\quad \text{(K) } -5\quad \text{(L) } 6\quad \text{(M) } -6\quad \text{(N) } 3+2i\quad \text{(O) } 3-2i\quad \$ (Error compiling LaTeX. Unknown error_msg)

$\text{(P) } \frac{-3+i\sqrt{3}}{2}\quad \text{(Q) } 8\quad \text{(R) } -8\qquad \text{(S) } 12\quad \text{(T) } -12\quad \text{(U) } 42\quad \$ (Error compiling LaTeX. Unknown error_msg)

$\text{(V) Ying} \quad \text{(W) } 207$

Solution