heytrevoreun
heytrevoreun heytrevoreun
  • 11-10-2021
  • Mathematics
contestada

Write the quadratic equation that has roots (-1-square root 2)/3 and (-1+square root 2)/3 if its coefficient with x^2 is equal to... 1

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sqdancefan
sqdancefan sqdancefan
  • 13-10-2021

9514 1404 393

Answer:

  x² +2/3x -1/9 = 0

Step-by-step explanation:

The quadratic with roots p and q can be written as ...

  (x -p)(x -q) = 0

  x² -(p+q)x +pq = 0

For p=(-1-√2)/3 and q=(-1+√2)/3, we have ...

  p +q = (-1-√2)/3 +(-1+√2)/3 = -2/3

  pq = ((-1-√2)/3)((-1+√2)/3) = (1 -2)/9 = -1/9

Then the quadratic is ...

  x² +2/3x -1/9 = 0

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