Bunuel wrote:
In the equation x^2 + mx + n = 0, x is a variable and m and n are constants. What is the value of n ?
(1) x + 2 is a factor of x^2 + mx + n
(2) The equation x^2 + mx + n = 0 has only one root
We need to determine the value of n.
Statement One Alone:
x + 2 is a factor of x^2 + mx + n.
Let f(x) = x^2 + mx + n. If x + 2 is a factor of x^2 + mx + n, then by the factor theorem, f(-2) = 0. That is, (-2)^2 + m(-2) + n = 0 or 4 - 2m + n = 0. However, since we don’t know the value of m, we can’t
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