Question

If a,B are ZEROES of 2X^2-4x+5 find values a^2+B^2?

Answer 1

$hey \: mate \: here \: is \: your \: answer$
$p(x) = 2x {}^{2} - 4x + 5$
$the \: zeros \: of \: the \: polynomial \: are \: a \: and \: b$
$sum \: of \: zeros \: = \frac{ - b}{a}$
$a + b = \frac{ - ( - 4)}{2}$
$a + b = \frac{ 4}{2}$
$a + b = 2 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: - (1)$

$product \: of \: zeros \: = \frac{c}{a}$
$ab = \frac{5}{2} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: -(2)$



$the \: value \: of \: a {}^{2} + b {}^{2} =$
${a}^{2} + b {}^{2} = (a + b) {}^{2} - 2ab$
$on \: putting \: the \: value \: of \: a + \: b \: and \: ab$
$\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = (2) {}^{2} - 2( \frac{5}{2} )$
$\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = 4 - 5$
$\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = - 1$