Question

quanto é x²-x-20=0?​

Answer 1

x² -x -20=0 => a=1, b=-1, c=-20
∆=b² -4.a.c = (-1)² -4.1.(-20)= 1 +80= 81
√∆= √81 = 9
x= -b±√∆/2a
x= -(-1)±9/2.1
x= 1±9/2
x' =1+9/2 = 10/2= 5 ✓
x" =1-9/2 = -8/2= -4 ✓

Answer 2

$\large\boxed{\begin{array}{l} \rm \: x {}^{2} - x - 20 = 0 \\ \\ \rightarrow \begin{cases} \rm \: a = 1 \\ \rm \: b = - 1 \\ \rm \: c = - 20\end{cases} \\ \\ \rm\Delta = b {}^{2} - 4 \cdot{a}\cdot{c} \\ \Delta = ( - 1) {}^{2} - 4 \cdot1 \cdot( - 20 ) \\ \Delta = 1 + 80 \\\Delta = 81 \\ \\ \rm \: x = \dfrac{ - b \pm \sqrt{\Delta} }{2 \cdot{a}} \\ \\ \rm \: x = \dfrac{ - ( - 1) \pm \sqrt{81} }{2 \cdot1} \\ \\ \rm \: x = \dfrac{1 \pm9}{2} \begin{cases} \rm \: x_1 = \dfrac{1 + 9}{2} = \dfrac{10}{2} = 5 \\ \\ \rm \: x _2 = \dfrac{1 - 9}{2} = \dfrac{ - 8}{2} = - 4\end{cases} \end{array}}$