Question

X^2-8x+19=0 quad formula

Answer 1

$\huge\blue{\bf{Question:}}$

$\bf Find \: the \: roots \: of \: the \\ \bf quadratic \: equation : \\ \bf {x}^{2} - 8x + 19 = 0 \\ \bf using \: quadratic \: formula$

$\huge\blue{\bf{Answer:}}$

$\bf Quadratic \: formula : \\ \\ \bf \frac{ - b ± \sqrt{ {b}^{2} - 4ac } }{2a} \\ \\ \bf Here \: \: \: a = 1 ,\: \: \: \: b = - 8 ,\: \: \: c = 19 \\ \\ \bf {b}^{2} - 4ac = {( - 8)}^{2} - 4(1)(19) \\ \bf = 64 - 76 \\ \bf = - 12 \\ \bf \therefore \sqrt{ {b}^{2} - 4ac } = \sqrt{ - 12} = - 2 \sqrt{3} \\ \\ \bf \implies \frac{- ( - 8) ± ( - 2 \sqrt{3} )}{2(1)} \\ \\ \bf = \frac{8 + ( - 2 \sqrt{3} )}{2} \: \: \: \: \: \frac{8 - ( - 2 \sqrt{3} )}{2} \\ \\ \bf = \frac{\cancel{8}^{4} - 2 \sqrt{3} }{ \cancel{2}} \: \: \: \: \: \frac{ \cancel{8}^{4} + 2 \sqrt{3} }{ \cancel{2}} \\ \\ \bf = 4 - 2 \sqrt{3} \: \: \: \: \: 4 + 2 \sqrt{3} \\ \\ \bf \therefore The \: roots \: are : \\ \bf 4 - 2 \sqrt{3} \: \: \: and \: \: \: 4 + 2 \sqrt{3}$

$\huge\blue{\bf{Hope~it~helps..!!}}$