2006
Mathematics
67ca00ce0c643c71d77dee1f
If y = x2 - x - 12, find the range of values of x for which y ≥ 0
A.
x < -3 0r x > 4
B.
x ≤ -3 or x ≥ 4
C.
-3 < x ≥ 4
D.
-3 ≤ x ≤ 4
Correct Answer: x ≤ -3 or x ≥ 4
Explanation
y = x2 - x - 12 = (x - 4)(x + 3) ∴ x = 4 or x = -3 Checking the cases for y ≥ 0 We check values on the range x - 4 ≥ 0; x + 3 ≤ 0; x - 4 ≤ 0 and x + 3 ≥ 0 for the range which satisfies the inequality x2 - x - 12 ≥ 0. We find that the inequality is satisfied on the range x ≤ -3 and x ≥ 4.
y = x2 - x - 12 = (x - 4)(x + 3) ∴ x = 4 or x = -3 Checking the cases for y ≥ 0 We check values on the range x - 4 ≥ 0; x + 3 ≤ 0; x - 4 ≤ 0 and x + 3 ≥ 0 for the range which satisfies the inequality x2 - x - 12 ≥ 0. We find that the inequality is satisfied on the range x ≤ -3 and x ≥ 4.THIS WEEK's
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