Verified answer

a) m < 4 / 3 ✓

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• RESOLUÇÃO

y = 3x² - 2x • ( m - 1 )

Para que esta equação admita duas raízes reais e distintas o valor do discriminante delta, obrigatoriamente deverá ser maior que zero. ∆ > 0

• Identificando os coeficientes:

[tex]\begin{cases}\sf~a=3\\\\\sf~b=-2\\\\\sf~c=m-1\end{cases}[/tex]

• Calculando o discriminante delta:

[tex]\sf\Delta=b^2-4ac\\\\\sf\Delta=(-2)^2-4\cdot3+(m-1)\\\\\sf4-4\cdot3(m-1)>0\\\\\sf4-12(m-1)>0\\\\\sf4-12m+12>0\\\\\sf16-12m>0\\\\\sf-12m>-16\\\\\sf~m<\frac{-\diagup\!\!\!\!\!\!12}{-\diagup\!\!\!\!\!\!16}\\\\\boxed{\sf~m<\frac{4}{3}}~\checkmark[/tex]

✨ [tex]\Large\mathscr{\blue{Per:~Dan}}[/tex] ✨