1. The roots of a quadratic equation

Can anyone kindly help me with the following please?

The roots of the equation x2 + 3x − 2 = 0 are α and β. Form a new equation with roots:

(a) α - 1 and β + 2

(b) α +2 and β + 1

The sum of the new roots is easy but I am finding the product of the new roots difficult.

2. Originally Posted by yobacul
Can anyone kindly help me with the following please?

The roots of the equation x2 + 3x − 2 = 0 are α and β. Form a new equation with roots:

(a) α - 1 and β + 2

(b) α +2 and β + 1

The sum of the new roots is easy but I am finding the product of the new roots difficult.

The roots are $\displaystyle \alpha = \frac{-3 + \sqrt{17}}{2}$ and $\displaystyle \beta = \frac{-3 - \sqrt{17}}{2}$.
(a) $\displaystyle \alpha - 1 = \frac{-5 + \sqrt{17}}{2}$ and $\displaystyle \beta + 2 = \frac{1 - \sqrt{17}}{2}$.
So a new equation is $\displaystyle \left( x + \frac{5 - \sqrt{17}}{2} \right) \cdot \left( x - \frac{1 - \sqrt{17}}{2}\right) = 0 \Rightarrow \, ....$