Question

Calcular o discriminante de cada equação
a)X2-4X-5=0
B)-X2+X+12=0
C)-X2+6×-5=0

Answer 1

Resposta:

a)

$Aplicando~a~f\'{o}rmula~de~Bhaskara~para~x^{2}-4x-5=0~~\\e~comparando~com~(a)x^{2}+(b)x+(c)=0,~temos~a=1{;}~b=-4~e~c=-5\\\\\Delta=(b)^{2}-4(a)(c)=(-4)^{2}-4(1)(-5)=16-(-20)=36$

b)

$Aplicando~a~f\'{o}rmula~de~Bhaskara~para~-x^{2}+x+12=0~~\\e~comparando~com~(a)x^{2}+(b)x+(c)=0,~temos~a=-1{;}~b=1~e~c=12\\\\\Delta=(b)^{2}-4(a)(c)=(1)^{2}-4(-1)(12)=1-(-48)=49$

c)

$Aplicando~a~f\'{o}rmula~de~Bhaskara~para~-x^{2}+6x-5=0~~\\e~comparando~com~(a)x^{2}+(b)x+(c)=0,~temos~a=-1{;}~b=6~e~c=-5\\\\\Delta=(b)^{2}-4(a)(c)=(6)^{2}-4(-1)(-5)=36-(20)=16$