résoudre 2x^2-10x + 24 = 13, 5

Bonsoir,

2x^2 - 10x + 24 = 13,5
2x^2 - 10x + 24 - 13,5 = 0
2x^2 - 10x + 10,5 = 0

Delta = (-10)^2 - 4 * 2 * 10,5
Delta = 100 - 84
Delta = 16
Vdelta = V16 = 4 > 0 donc deux solutions possibles

X1 = (10 - 4)/(2 * 2) = 6/4 = 3/2
X2 = (10 + 4)/(2 * 2) = 14/4 = 7/2

Bonsoir

♧ On a :

2x² - 10x + 24 = 13,5
2x² - 10x + 24 - 13,5 = 0
2x² - 10x + 10,5 = 0

♧ Calcul du discriminant Δ :

Δ = b² - 4ac
Δ= (-10)²- 4×2×10,5
Δ = 16

♧ On a Δ > 0 donc l'équation admet 2 solutions :

X1 = -b+√Δ/2a = 10+4/4 = 14/4 = 7/2
X2 = -b-√Δ/2a = 10-4/4 = 6/4 = 3/2

S = {7/2;3/2}

Voilà ^^