Five times a positive integer is 3 less than twice its square. Find the integer.
Correct Answer:
C. 3
Explanation:
To find the positive integer, let it be represented by x. According to the problem, five times the integer (5x) is equal to 3 less than twice its square (2x² - 3). This gives the quadratic equation: 2x² - 5x - 3 = 0.
By factoring the quadratic equation, we get (2x + 1)(x - 3) = 0. This results in two possible solutions for x: -1/2 and 3. Since the problem specifies that the integer must be positive, we discard -1/2. Therefore, the integer is 3.
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