Solve the inequality 2x^2 − 5x + 3 ≤ 0.

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Multiple Choice

Solve the inequality 2x^2 − 5x + 3 ≤ 0.

Explanation:
To solve a quadratic inequality like 2x^2 − 5x + 3 ≤ 0, find where the parabola is at or below the x-axis. Factor the quadratic: 2x^2 − 5x + 3 = (2x − 3)(x − 1). The zeros are x = 3/2 and x = 1. Since the leading coefficient is positive, the parabola opens upward. A sign check shows the product (2x − 3)(x − 1) is negative between the roots and zero at the roots. Outside that interval, the product is positive. Therefore, the inequality holds for x in [1, 3/2].

To solve a quadratic inequality like 2x^2 − 5x + 3 ≤ 0, find where the parabola is at or below the x-axis. Factor the quadratic: 2x^2 − 5x + 3 = (2x − 3)(x − 1). The zeros are x = 3/2 and x = 1. Since the leading coefficient is positive, the parabola opens upward. A sign check shows the product (2x − 3)(x − 1) is negative between the roots and zero at the roots. Outside that interval, the product is positive. Therefore, the inequality holds for x in [1, 3/2].

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