Question

Find the zeros of the polynomial the sum of whose zeros is under root 2 and their product of is -12 hence find the zeros of the polynomial

Answer 1

$for \: a \: polynomial \: a {x}^{2} + bx + c = 0 \\ sum \: of \: roots \: = \frac{ - b}{a} \\ product \: of \: roots = \frac{c}{a} \\ given \\ sum \: of \: roots = \frac{ - b}{a} = \sqrt{2} \\ product \: of \: roots = \frac{c}{a} = - 12 \\ now \: the \: polynomial \: is \\ {x}^{2} - \sqrt{2} x - 12 = 0 \\ wkt \: x = \frac{ - b + | \sqrt{ ( {b}^{2} - 4ac) \: \: \: | }}{2a} \\ x = \frac{1}{ \sqrt{2} } + \sqrt{13} \\ x = \frac{1}{ \sqrt{2} } - \sqrt{13}$
hope it helps