Answer:
Step-by-step explanation:
1) x² + 3x + 1 = 0
a = 1 b = 3 c = 1
=> Δ = b² - 4ac = 9 - 4.1.1 = 5 > 0
so the quadratic equation have 2 solutions
=> x = [tex]\frac{-3+\sqrt{5} }{4}[/tex]
or x = [tex]\frac{-3-\sqrt{5} }{4}[/tex]
2) x² + 4x - 8 = 0
a = 1 b' = 2 c = -8
Δ' = b'² - ac = 4 - 1.(-8) = 12 > 0
so the quadratic equation have 2 solutions
=> x = [tex]\frac{-2+\sqrt{12} }{1}=-2+\sqrt{12}[/tex]
or x = [tex]-2-\sqrt{12}[/tex]
3) x² - 5x -12 = 0
a = 1 b = -5 c = -12
Δ = b² - 4ac = 25 - 4.1.(-12) = 25 + 48 = 73 > 0
so the quadratic equation have 2 solutions
=> x = [tex]\frac{5+\sqrt{73} }{2}[/tex]
or x = [tex]\frac{5-\sqrt{73} }{2}[/tex]
