Question

quantas raízes tem essa funçao x²-4x+10,-6 < x < 10 , -10 < y < 25

Answer 1

Bom dia Mary!

Solução!

$x^{2} -4x+10=0$

$a=1\\\\ b=-4\\\\ c=10$

Vamos substituir esses coeficientes a,b e c na formula de Bhaskara.

$x= \dfrac{-b\pm \sqrt{b^{2} -4.a.c} }{2.a}\\\\\\ x= \dfrac{-(-4)\pm \sqrt{(-4)^{2} -4.1.10} }{2.1}\\\\\\ x= \dfrac{4\pm \sqrt{16-40} }{2}\\\\\\ x= \dfrac{4\pm \sqrt{-24} }{2}\\\\\\ x= \dfrac{4\pm i\sqrt{24} }{2}\\\\\\ x= \dfrac{4\pm 2i\sqrt{6} }{2}\\\\\\ x=2( \dfrac{2\pm i\sqrt{6} }{2})\\\\\\ x=(2\pm i\sqrt{6})\\\\\\\\\\ Resposta~~~\\\\\\ Duas~~Raizes~~complexas\\\\\ x_{1}=2+i \sqrt{6}\\\\\ x_{2}=2-i \sqrt{6}$

Bom dia!
Bons estudos!