Question

21. Se r' e r", são as raízes da equação
3x² – 2x – 8 = 0, sendo x'< x", então
3.x"2 – 2x'-8 é igual a:
a) 2/3
b) 8/3
a=3x
lear
c) 16/3
d) 20/3​

Answer 1

Resposta:

D) 20/3

Explicação passo-a-passo:

$\Delta = b^2-4ac\\\Delta=(-2)^2-4(3)(-8)\\\Delta=4+96\\\Delta=100\\\\r'=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+10}{2(3)}=\frac{2+10}{6}=\frac{12}{6}=2\\\\r''=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-10}{2(3)}=\frac{2-10}{6}=\frac{8}{6}=\frac{4}{3}\\\\x'<x'', r''<r'\\x' = r''\\x''= r'\\\\3(x'')^2-2x'-8\\3(2)^2-2(\frac{4}{3})-8\\3\cdot4-\frac{8}{3}-8\\12-\frac{8}{3}-8\\-\frac{8}{3}-4\\\\-\frac{8}{3}-\frac{12}{3}\\\\\frac{-20}{3}$

Bons estudos!