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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
