Solve x^2 - 3x - 4 ≥ 0.

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Multiple Choice

Solve x^2 - 3x - 4 ≥ 0.

Explanation:
A quadratic inequality like this is solved by finding where the parabola is at or above the x-axis. Since the leading coefficient is positive, the graph opens upward, so the expression is nonnegative outside the interval between its zeros. Factor the quadratic: x^2 - 3x - 4 = (x - 4)(x + 1). The zeros are -1 and 4. Because the parabola opens upward, the product (x - 4)(x + 1) is nonnegative when x ≤ -1 or x ≥ 4 (endpoints included, since we allow equality). Between -1 and 4 the product is negative, so those values do not satisfy the inequality.

A quadratic inequality like this is solved by finding where the parabola is at or above the x-axis. Since the leading coefficient is positive, the graph opens upward, so the expression is nonnegative outside the interval between its zeros.

Factor the quadratic: x^2 - 3x - 4 = (x - 4)(x + 1). The zeros are -1 and 4. Because the parabola opens upward, the product (x - 4)(x + 1) is nonnegative when x ≤ -1 or x ≥ 4 (endpoints included, since we allow equality).

Between -1 and 4 the product is negative, so those values do not satisfy the inequality.

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