a) Δ = 5²- 4* 2 * (-12) = 25 + 96 =121 √121 = 11
x₁ = [tex]\frac{-5-11}{4}[/tex] = -4
x₂ = [tex]\frac{-5+11}{4}[/tex] = [tex]\frac{-6}{4}[/tex] =- [tex]\frac{3}{2}[/tex]
b) 3x² -7x - 20 = 0
Δ= (-7)² - 4 * 3 * (-20) = 49 + 240 = 289 √289 = 17
x₁ = [tex]\frac{7-17}{6} = \frac{-10}{6} = - \frac{5}{3}[/tex]
x₂ = [tex]\frac{7+17}{6} = \frac{24}{6} =4\\[/tex]
c) 9x² - 12x +4 =0
Δ= (-12)² - 4 * 9 * 4 = 144- 144 = 0
x₁ = [tex]\frac{12}{18} = \frac{2}{3}[/tex]
d) 49x² - 4x = = 0
Δ = (-4)² - 4 * 49 * 0 = 16 √16 = 4
x₁ = [tex]\frac{4 - 4}{98} = 0[/tex]
x₂ = [tex]\frac{4+4}{98} = \frac{16}{98} =\frac{1}{32}[/tex]
e) 16x² + 25 - 40x = 0
Δ = (-40)² - 4 * 16 * 25 = 1600 - 1600 =0
x₁ = [tex]\frac{40}{32} = \frac{5}{4}[/tex]
