Question

which equation has the solutions $x = 1pmsqrt{5}$?\
\\(\bigcirc\\) $x^2 + 2x + 4 = 0$\
\\(\bigcirc\\) $x^2 - 2x + 4 = 0$\
\\(\bigcirc\\) $x^2 + 2x - 4 = 0$\
\\(\bigcirc\\) $x^2 - 2x - 4 = 0$

Explanation:

Step1: Start from given solutions

$x = 1 \pm \sqrt{5}$

Step2: Rearrange to factor form

$x - 1 = \pm \sqrt{5}$
Square both sides: $(x - 1)^2 = (\pm \sqrt{5})^2$

Step3: Expand and simplify

$(x - 1)^2 = 5$
$x^2 - 2x + 1 = 5$
$x^2 - 2x - 4 = 0$

Answer:

$x^2 - 2x - 4 = 0$