Question

if one root of quadratic education is x^+6x+k is h+2✓6 find h and k

Answer 1

$given \: \: one \: root \: is \: h + 2 \sqrt{6} \\ therefore \: other \: root \: is \: h - 2 \sqrt{6 } \\ sum \: of \: roots \: \: (h + 2 \sqrt{6}) + (h - 2 \sqrt{6} ) \\ 2h = - 6 \\ h = - 3 \\ product \: of \: roots (h + 2 \sqrt{6})(h - 2 \sqrt{6} ) \: \: \\ {h}^{2} - 24 = k \\ k = {( - 3)}^{2} - 24 = - 15$