Odpowiedź:
a)
delta = b² - 4ac = (-4)² - 4 * (-1) * 3 = 16 + 12 = 28
[tex]\sqrt{delta}[/tex] = [tex]\sqrt{28}[/tex] = [tex]2\sqrt{7}[/tex]
[tex]x_{1}[/tex] = [tex]\frac{-b + \sqrt{delta} }{2a}[/tex] = [tex]\frac{4 + 2\sqrt{7} }{-2}[/tex] = -2-[tex]\sqrt{7}[/tex]
[tex]x_{2}[/tex] = [tex]\frac{-b - \sqrt{delta} }{2a}[/tex] = [tex]\frac{4 - 2\sqrt{7} }{-2}[/tex] = -2+[tex]\sqrt{7}[/tex]
b)
delta = 36 - 28 = 8
[tex]\sqrt{delta}[/tex] = [tex]2\sqrt{2}[/tex]
[tex]x_{1}[/tex] = [tex]\frac{6 + 2\sqrt{2} }{2}[/tex] = 3+[tex]\sqrt{2}[/tex]
[tex]x_{2}[/tex] = [tex]\frac{6 - 2\sqrt{2} }{2}[/tex] = 3-[tex]\sqrt{2}[/tex]
c)
delta = 1 + 8 = 9
[tex]\sqrt{delta}[/tex] = 3
[tex]x_{1}[/tex] = [tex]\frac{-1 + 3 }{-4}[/tex] = -0,5
[tex]x_{2}[/tex] = [tex]\frac{-1 - 3 }{-4}[/tex] = 1
