Question

solve the equation x²-2x-4=0 using
quadratic formula.​

Answer 1

x²−2x+4=0 has no real solutions, only complex ones, but the quadratic formula does work to give:

x = 1 ± i√3

$\sf{x}^{2} - 2x + 4 \: of \: the \: form \: {ax}^{2} + bx + c$

$\sf with \: a = 1b = - 2 \: and \: c = 4$

$\sf The \: quadratic \: formula \: gives \: us \: the \: solutions$

$\sf to \:   {x}^{2} −2x+4 \:  as:$

$\sf x = \frac{ - b ± \sqrt{ {b}^{2} - 4ac } }{2a}$

$\sf \implies \frac{2 \: ± \: \sqrt{ {2}^{2} - (4 \times 1 \times 4)} }{2}$

$\sf \implies \frac{2 \: ± \: \sqrt{ - 12} }{2}$

$\sf \implies \frac{2 \: ± \: 2 \sqrt{ - 3} }{2}$

$\sf \therefore 1 \: ± \: i \sqrt{3}$