Question

if
$if \alpha \: and \beta are \: the \: zeroes \: of \: polynomial \: p(x) = 3x { \: }^{2} - 14x \: + 15 \: find \: the \: value \: of \: \alpha {}^{2} + \beta {}^{2}$
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Answer 1

Step-by-step explanation:

$\alpha \: and \: \beta \: are \: zeros....... \\ \alpha + \beta = \frac{ - b}{a} = \frac{14}{3}........(1) \\ \alpha \beta = \frac{c}{a} = \frac{15}{3} = 5 \\ \alpha = \frac{5}{ \beta } .........(2) \\ put \: (2) \: in \: (1) = > \\ \frac{5}{ \beta } + \beta = \frac{14}{3} \\ 5 + { \beta }^{2} = \frac{14}{3} \beta \\ 15 + 3 { \beta }^{2} = 14 \beta \\ 3 { \beta }^{2} - 14 \beta + 15 = 0 \\ from \: here \: you \: can \: solve \: futher....$