Question

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

Answer 1

9514 1404 393

Answer:

x² +2/3x -1/9 = 0

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