Question

Calcule as raizes de x²-9×+14=0

Answer 1

$\large\boxed{\begin{array}{l} \rm \: x {}^{2} - 9x + 14 = 0 \\ \\ \Rightarrow \begin{cases} \rm \: a = 1 \\ \rm \: b = - 9 \\ \rm \: c = 14\end{cases} \\ \\ \rm\Delta = b {}^{2} - 4ac \\\Delta = ( - 9) {}^{2} - 4 \: . \: 1 \: . \: 14 \\ \Delta = 81 - 56 \\ \Delta = 25 \\ \\ \rm \: x = \dfrac{ - b \pm \sqrt{\Delta} }{2a} \\ \\ \rm \: x = \dfrac{ - ( - 9) \pm \sqrt{25} }{2.1} \\ \\ \rm \: x = \dfrac{9 \pm5}{2} \begin{cases} \rm \: x_1 = \dfrac{9 + 5}{2} = \dfrac{14}{2} = \boxed{7} \checkmark \\ \\ \rm \:x_2 = \dfrac{9 - 5}{2} = \dfrac{4}{2} = \boxed{2} \checkmark\end{cases}\end{array}}$