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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