Question

As raízes da equação x 2 + bx + c = 0 são 2 e − 4. Nesse caso, determine o valor de b – c.

Answer 1

$x^2+bx+c=0$

$x=2$  e  $x=-4$

$\left \{ {{2^2+2b+c=0} \atop {(-4)^2-4b+c=0}} \right.$

$\left \{ {{4+2b+c=0} \atop {16-4b+c=0}} \right.$

$\left \{ {{c=-4-2b} \atop {-4b=-16-(-4-2b)}} \right.$

$\left \{ {{c=-4-2b} \atop {-6b=-12}} \right.$

$\left \{ {{c=-4-2*2} \atop {b=2}} \right.$

$\left \{ {{c=-8} \atop {b=2}} \right.$

$b-c=2-(-8)=10$