Question

3x2-(m+1)x+m-2

duas raízes reais iguais

Answer 1

Oie, tudo bom?

$3x {}^{2} - (m + 1)x + m - 2$

$\boxed{a = 3\: , \: b = - (m + 1) \: , \: c = m - 2}$

$∆ = b {}^{2} - 4ac \\ ( - (m + 1)) {}^{2} - 4 \: . \: 3(m - 2) =0 \\ (m + 1) {}^{2} - 12(m - 2) =0 \\ m {}^{2} + 2m + 1 - 12m + 24 = 0 \\ m {}^{2} - 10m + 25 = 0 \\ m {}^{2} - 2 \: . \: m \: . \: 5 + 5 {}^{2} = 0 \\ (m - 5) {}^{2} = 0 \\ m - 5 = 0 \\ \boxed{m = 5}$

Att. NLE Top Shotta