Odpowiedź:
zad 1
c)
- 3x² + 2x + 9 = 0
a = - 3 , b = 2 , c = 9
Δ = b² - 4ac = 2² - 4 * (- 3) * 9 = 4 + 108 = 112
√Δ = √112 = √(16 * 7) = 4√7
x₁ = ( - b - √Δ)/2a = (- 2 - 4√7)/(- 6) = - 2(1 + 2√7)/(- 6) = (1 + 2√7)/3
x₂ = (- b + √Δ)/2a = (- 2 + 4√7)/(- 6) = - 2( 1 - 2√7)/(- 6) = (1 - √7)/3
d)
4x² + 20x + 25 = 0
a = 4 , b = 20 , c = 25
Δ = b² - 4ac = 20² - 4 * 4 * 25 = 400 - 400 = 0
x₁ = x₂ = - b/2a = - 20/8 = - 2 4/8 = - 2 1/2
e)
6x² - 5/2x + 1/4 = 0
a = 6 , b = 5/2 , c = 1/4
Δ = b² - 4ac = (5/2)² - 4 * 6 * 1/4 = 25/4 - 24/4 = 1/4
√Δ = √(1/4) = 1/2
x₁ = ( - b - √Δ)/2a = ( - 5/2 - 1/2)/12 = - 6/2 : 12 = - 3/12 = - 1/4
x₂ = (- b + √Δ)/2a = (- 5/2 + 1/2)/12 = - 4/2 : 12 = - 2/12 = - 1/6
