1) Aplicamos formula general.
Sea: [tex] Ax^{2} +BX+C=0[/tex]
Formula general: [tex]( x_{1} ; x_{2} )= \frac{-B+- \sqrt{ B^{2}-4AC } }{2A} [/tex] ; donde x1 y x2 son las raices de la ecuacion.
[tex] x^{2} -11x-30=0[/tex] ---> A= 1 ; B = -11 ; C = -30
Luego: [tex]( x_{1} ; x_{2} )= \frac{-(-11)+- \sqrt{ (-11)^{2}-4(1)(-30) } }{2(1)} [/tex]
= [tex]\frac{-11+- \sqrt{ 121+120 } }{2}[/tex]
= [tex]\frac{-11+- \sqrt{ 241 } }{2}[/tex]
Luego: [tex] x_{1}= \frac{-11+ \sqrt{ 241 } }{2}[/tex] y [tex] x_{2}= \frac{-11- \sqrt{ 241 } }{2}[/tex]
2) Aplicamos aspa simple:
[tex] x^{2} -9x-220=0[/tex]
x -20 ---> -20x
x +11 ---> +11x
-9x
Luego: (x - 20)(x + 11) = 0 ----> x - 20 = 0 v x + 11 = 0
x = 20 v x = -11
Por tanto, C.s.={-11 ; 20}
3) Aspa simple:
[tex] x^{2} -15x+56=0[/tex]
x -8 ---> -8x
x -7 ---> -7x
-15x
Luego: (x - 8)(x - 7) = 0 ------> x - 8 = 0 v x - 7 = 0
x = 8 v x = 7
Por tanto; C.s.={7 ; 8}
