1. Form the Quadratic Equation whose roots are Alpha = 2, Beta = 5
Let `alpha = 2` and `beta = 5`
Then, the sum of the roots `= alpha + beta = (2)+(5) = 7`
and the Product of the roots `= alpha * beta = (2)*(5) = 10`
The Equation with roots `alpha` and `beta` is given by
`X^2  (alpha+beta)X + alpha*beta = 0`
`:.` The required equation
`X^2  (7)X + (10) = 0`
2. Form the Quadratic Equation whose roots are Alpha = 1/2, Beta = +2/3
Let `alpha = 1/2` and `beta = +2/3`
Then, the sum of the roots `= alpha + beta = (1/2)+(+2/3) = 1/6`
and the Product of the roots `= alpha * beta = (1/2)*(+2/3) = 1/3`
The Equation with roots `alpha` and `beta` is given by
`X^2  (alpha+beta)X + alpha*beta = 0`
`:.` The required equation
`X^2  (1/6)X + (1/3) = 0`
