Question

11. Work backwards to write a quadratic equation that will have solutions of x = 12 and x = 2.

Answer 1

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Answer:  $\textsf{x}^2\textsf{ - 14x + 24}$

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Given:  $\textsf{x = 12 and x = 2}$

Find: $\textsf{Determine the quadratic equation}$

Solution:  In order to determine the quadratic equation we need to move the integers onto the side where x is and then distribute.

Move the integers

• Solution #1

• $\textsf{x - 12 = 12 - 12}$

• $\textsf{x - 12 = 0}$

• Solution #2

• $\textsf{x - 2 = 2 - 2}$

• $\textsf{x - 2 = 0}$

Create and expression and distribute

• $\textsf{(x - 12)(x - 2) = 0}$

• $\textsf{(x * x) + (x * -2) + (-12 * x) + (-12 * -2) = 0}$

• $\textsf{x}^2\textsf{ - 2x - 12x + 24 = 0}$

• $\textsf{x}^2\textsf{ - 14x + 24 = 0}$

Therefore, after completing the steps we were able to determine that the quadratic equation that will have solutions of x = 12 and x = 2 is x^2 - 14x + 24.