NandishSS wrote:In the xy-coordinate plane, the graph of y=x^2−kx−6, where k is a constant, crosses the x-axis at two points. What is the value of k?
(1) For each of the two points where the graph crosses the x-axis, the x-coordinate is an integer.
(2) The graph crosses the x-axis at (1,0).
Statement 1:
Case 1: y = (x+2)(x-3) = x²-x-6.
In this case, k=1.
Case 2: y = (x+1)(x-6) = x²-5x-6.
In this case, k=5.
Since k can be different values, INSUFFICIENT.
Statement 2:
Plugging x=1 and y=0 into y = x²-kx-6, we get:
0 = 1² - (k)(1) - 6
0 = -k - 5
k = -5.
SUFFICIENT.
The correct answer is
B.
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