Question

If p and q are the zeroes of the polynomial f(x)=2x2-6x+3 find the value of p/q+q/p

Answer 1

$since \: p \: and \: q \: are \: zeros \: of \: f(x)$
$p + q = \frac{ - ( - 6)}{2} = 3$
$p \times q = \frac{3}{2}$
$now \: \frac{p}{q} + \frac{q}{p} = \frac{ {p}^{2} + {q}^{2} }{p \times q} = \frac{ {(p + q)}^{2} - 2pq}{pq}$
$= \frac{ {3}^{2} - 2 \times \frac{3}{2} }{ \frac{3}{2} }$
$= \frac{9 - 3}{ \frac{3}{2} }$
$= \frac{6 \times 2}{3}$
$= 4$