Question

If alpha beta are roots of the polynomial f(x) = x2-px+q then Find value of

1) alpha2 + beta2

2) 1/alpha + 1/beta

3) alpha/beta + beta/alpha

Answer 1

$\alpha + \beta = p$
$\alpha \beta = q$
1.
$\: { \alpha }^{2} + { \beta }^{2} = {( \alpha + \beta )}^{2} - 2 \alpha \beta$
$= {p}^{2} - 2q$
2.
$\frac{1}{ \alpha } + \frac{1}{ \beta }$
$= \frac{ \alpha + \beta }{ \alpha \beta }$
$= \frac{p}{q}$
3.
$\frac{ \alpha }{ \beta } + \frac{ \beta }{ \alpha } = \frac{ { \alpha }^{2} + { \beta }^{2} }{ \alpha \beta } = \frac{ {p}^{2} - 2q }{q}$