Question

Write the quadratic equation that has roots (-1-√2)/3 and (-1+√2)/3 , if it's coefficient with x^2 is equal to

Answer 1

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Answer:

  (a) x² +2/3x -1/9 = 0

  (b) 9x² +6x -1 = 0

Step-by-step explanation:

The product of quadratic factors can be expanded to give ...

  (x -p)(x -q) = x² -(p+q)x +pq

Then the coefficients of x² +bx +c = 0 will be ...

  b = -((-1-√2)/3 +(-1+√2)/3)) = 2/3

  c = ((-1-√2)/3)·((-1+√2)/3) = (-1/3)² -(√2/3)²) = 1/9 -2/9 = -1/9

a) The quadratic with leading coefficient 1 is ...

  x² +2/3x -1/9 = 0

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b) Multiplying that by 9 gives ...

  9x² +6x -1 = 0