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For a certain quadratic equation, ax2 + bx + c = 0, the 2 solutions are x = ¾ and x =-⅖ . Which of the following could be factors of ax2 + bx + c?

Correct answer: A. (4x - 3) AND (5x + 2)

  • A. (4x - 3) AND (5x + 2)
  • B. (4x^2) AND (5x + 3)
  • C. (4x + 2) AND (5x - 3)
  • D. (4x + 3) AND (5x - 2)
  • E. (4x + 3) AND (5x + 2)

Explanation

To find the factors of the quadratic equation ax2 + bx + c = 0, use the solutions x = 3/4 and x = -2/5. For each solution x = a/b, a factor is of the form (bx - a). Thus, for x = 3/4, the factor is (4x - 3), and for x = -2/5, the factor is (5x + 2). Multiplying these factors gives the original quadratic equation. Other options contain factors that do not match the solutions provided, making them incorrect.

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About Quantitative Reasoning

Quantitative reasoning applies arithmetic and basic algebra to numerical relationships, including percentages, ratios, averages, fractions, proportions, profit and loss, rates, time, work and measurement. Questions focus on translating words into equations, choosing an efficient method and checking whether the result is numerically reasonable.

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