Question

scrr, com calculos prfvr
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Answer 1

Resposta:

Explicação passo-a-passo:

a = 1-t

b = 4

c = -2

Cálculo do discriminante

$\Delta=b^{2}-4.a.c\\\\ \Delta=4^{2}-4.(1-t).(-2)\\ \\\Delta=16+8.(1-t)\\\\\Delta=16+8-8t\\\\\Delta=24-8t$

temos 3 casos

Caso 1 : 2 raízes reais e distintas  ($\Delta>0$)

$\Delta>0\\24-8t>0\\-8t>-24\\8t<24\\\\t<\dfrac{24}{8}\\\\t<3$

Caso 2: 2 raízes reais e iguais  ($\Delta=0$)

$\Delta=0\\24-8t=0\\-8t=-24\\8t=24\\\\t=\dfrac{24}{8}\\\\t=3$

Caso 3: sem raízes reais ($\Delta<0$)

$\Delta<0\\24-8t<0\\-8t<-24\\8t>24\\\\t>\dfrac{24}{8}\\\\t>3$