Answer:
alpha/Beta and Beta/alpha
Explanation:
If the roots of the quadratic equation x^2 + 2x + 2 = 0 are 1/alpha and 1/Beta, then we can write the quadratic equation in factored form as:
(x - 1/alpha)(x - 1/Beta) = 0
Expanding this, we get:
x^2 - (1/alpha + 1/Beta)x + 1/alpha * 1/Beta = 0
This is the quadratic equation whose roots are 1/alpha and 1/Beta.
For the second part of the question, we want to find the quadratic equation whose roots are alpha and Beta. To do this, we can simply reverse the roles of alpha and Beta in the original equation:
(x - alpha)(x - Beta) = 0
Expanding this, we get:
x^2 - (alpha + Beta)x + alpha * Beta = 0
This is the quadratic equation whose roots are alpha and Beta.
For the third part of the question, we want to find the quadratic equation whose roots are alpha/Beta and Beta/alpha. To do this, we can use the same method as before, but with alpha/Beta and Beta/alpha in place of alpha and Beta:
(x - alpha/Beta)(x - Beta/alpha) = 0
Expanding this, we get:
x^2 - (alpha/Beta + Beta/alpha)x + alpha/Beta * Beta/alpha = 0
This is the quadratic equation whose roots are alpha/Beta and Beta/alpha.