Final answer:
The quadratic equation with roots (-1-√2)/3 and (-1+√2)/3 and a leading coefficient of 9 can be written by multiplying out 9(x - (-1-√2)/3)(x - (-1+√2)/3).
Step-by-step explanation:
The student is asked to write a quadratic equation whose roots are (-1-√2)/3 and (-1+√2)/3, and whose leading coefficient, the coefficient with x^2, is 9. To find such an equation, we use the fact that if α and β are the roots of the quadratic equation ax^2 + bx + c = 0, then the equation can be expressed as a(x - α)(x - β) = 0. Plugging in the roots provided and the leading coefficient, we get the equation 9(x - (-1-√2)/3)(x - (-1+√2)/3) = 0.
By simplifying this equation, we will arrive at the desired quadratic equation.