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Answer:
a) -3/5x² -2/5x +1/15 = 0
b) √3/3x² +2√3/9x -√3/27 = 0
Step-by-step explanation:
The quadratic equation of interest is of the form ...
(leading coefficient)(x^2 -(sum of roots)x +(product of roots)) = 0
The sum of the given roots is ...
(-1 +√2)/3 +(-1 -√2)/3 = -2/3
The product of the given roots is ...
(-1 +√2)/3×(-1 -√2)/3 = ((-1)² -(√2)²)/3² = -1/9
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a) The quadratic is ...
(-3/5)(x² +2/3x -1/9) = -3/5x² -2/5x +1/15 = 0
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b) The quadratic is ...
(√3/3)(x² +2/3x -1/9) = √3/3x² +2√3/9x -√3/27 = 0
