[tex]\displaystyle \sf 3x^2-(m+1)x+m-2=0 \\\\ \text{para ra\'izes reais e iguais devemos ter }\Delta =0\\\\ b^2-4ac=0 \\\\ (-(m+1))^2-4\cdot 3\cdot (m-2)=0 \\\\ m^2+2m+1-12m+24 = 0 \\\\ m^2-10m+25 = 0 \\\\ (m-5)^2=0 \\\\ \large\boxed{\sf \ m = 5 \ }\checkmark[/tex]
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[tex]\displaystyle \sf 3x^2-(m+1)x+m-2=0 \\\\ \text{para ra\'izes reais e iguais devemos ter }\Delta =0\\\\ b^2-4ac=0 \\\\ (-(m+1))^2-4\cdot 3\cdot (m-2)=0 \\\\ m^2+2m+1-12m+24 = 0 \\\\ m^2-10m+25 = 0 \\\\ (m-5)^2=0 \\\\ \large\boxed{\sf \ m = 5 \ }\checkmark[/tex]