2.5.2 Sum of Roots and Product of Roots (Examples)

Example
The roots of $2x^2+3x-1=0$   are α and β.  Find the values of
(a) $(\alpha +1)(\beta +1)$
(b) $\frac{1}{\alpha }+\frac{1}{\beta }$
(c) ${\alpha }^2\beta +\alpha {\beta }^2$
(d) $\frac{\alpha }{\beta }+\frac{\beta }{\alpha }$

[Clue: ${\alpha }^2+{\beta }^2={(\alpha +\beta )}^2-2\alpha \beta$   ]

2.5.2a Forming New Quadratic Equation given a Quadratic Equation
Example
If the roots of $x^2-3x-7=0$   are α  and β  , find the equation whose roots are ${\alpha }^2\beta$   and $\alpha {\beta }^2$ .

Solution

Part 1 : Find SoR and PoR for the quadratic equation in the question




Part 2 : Form a new quadratic equation by finding SoR and PoR