Carcass wrote:
If \(x^2 + 5x - 6 = 0\) and \(x < 0\), which of the following is not equal to 0?
(A) \(x^2 + 4x- 12 \)
(B) \(x^2 - 5x - 6 \)
(C) \(x^2 + 7x + 6\)
(D) \(x^2 + 4x + 12\)
(E) All are equal to 0.
Given: \(x^2 + 5x - 6 = 0\)
Factor the left side: \((x + 6)(x - 1)\)
So, either \(x = -6\) or \(x = 1\)
Since we're told \(x < 0\), we know that \(x = -6\)
Now plug \(x = -6\) into each expression to see which one does NOT evaluate to 0.
(A) \(x^2 + 4x- 12 = (-6)^2 + 4(-6)- 12 = 36 - 24 - 12 = 0\). Eliminate answer choice A.
(B) \(x^2 - 5x - 6 =(-6)^2 - 5(-6) - 6 = 36 + 30 - 6 = 60 \)
Answer: B