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 $\alpha = \frac{-3 + \sqrt{17}}{2}$ and $\beta = \frac{-3 - \sqrt{17}}{2}$.

Use these to calculate the required new roots. Now construct new quadratic equations form these roots.

(a) $\alpha - 1 = \frac{-5 + \sqrt{17}}{2}$ and $\beta + 2 = \frac{1 - \sqrt{17}}{2}$.

So a new equation is $\left( x + \frac{5 - \sqrt{17}}{2} \right) \cdot \left( x - \frac{1 - \sqrt{17}}{2}\right) = 0 \Rightarrow \, ....$

3. ## The roots of a quadratic equation

Thanks for your reply. However, the teacher told us that we have to find the new quadratic equation without solving the previous; in the sense that we are required to make use of the sum of roots and product of roots of the original equation.