Question

If α and β are the roots of the quadratic equation of x2+7x+5=0. Find the value of α2+β2

Answer 1

⭐⭐HEY MATE HERE IS YOUR ANSWER ⭐⭐

$\alpha \: and \: \beta \: are \: roots \: then \:$
$\alpha + \beta = \frac{ - b}{a} \: and \\ \alpha \beta = \frac{c}{a}$
${x}^{2} + 7x + 5 = 0 \\ a{x}^{2} + bx + c = 0 \\ compare$
a=1;b=7;c=5

$hence \: \\ \alpha + \beta = - 7 \\ \alpha \beta = 5 \\ substitute \: these \: values \: in \: this \: \\ {( \alpha + \beta )}^{2} = { \alpha }^{2} + { \beta }^{2} + 2( \alpha \beta ) \\ { \alpha }^{2} + { \beta }^{2} = {( \alpha + \beta )}^{2} - 2( \alpha \beta ) \\ {( \alpha + \beta )}^{2} = { (- 7)}^{2} -2 (5) \\ {( \alpha + \beta )}^{2} = 49 - 10 \\ {( \alpha + \beta )}^{2} = 39$
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