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.