Question

Determine as raízes de cada equação abaixo

$a) {x}^{2}-x-20 = 0$
$b) {x}^{2} - x - 4 = 0$
(R: x' = 5 e x" = -4)
(R: x' = 4 ex" = -1)

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Answer 1

a)

$x^2-x-20=0\Longrightarrow a=1,\ b=-1,\ c=-20$

$\boxed{x=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}}\Longrightarrow x=\dfrac{1\pm\sqrt{81}}{2}=\dfrac{1\pm9}{2}$

$\Longrightarrow x=-4\ \text{ou}\ x=5\Longrightarrow\boxed{x=\{-4,5\}}$

b)

$x^2-x-4=0\Longrightarrow a=1,\ b=-1,\ c=-4$

$\boxed{x=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}}\Longrightarrow x=\dfrac{1\pm\sqrt{17}}{2}$

$\Longrightarrow x=\dfrac{1-\sqrt{17}}{2}\ \text{ou}\ x=\dfrac{1+\sqrt{17}}{2}\Longrightarrow\boxed{x=\left\{\dfrac{1-\sqrt{17}}{2},\dfrac{1+\sqrt{17}}{2}\right\}}$