[tex]3x^{2} - 4x + 1 = 0 \\ Δ = 16 - 4 \times 3 \times 1 = 16 - 12 = 4 \\ \sqrt{Δ} = 2 \\ x_{1} = \frac{4 - 2}{6} = \frac{1}{3} \\ x_{2} = \frac{4 + 2}{6} = 1[/tex]
[tex] {x}^{2} + 3x = 28 \\ x(x + 3) = 28 \\ x_{1} = 0 \\ x_{2} = - 3[/tex]
[tex]3 {x}^{2} + 17x - 6 = 0 \\ Δ = 289 - 4 \times 3 \times ( - 6) = 289 + 72 = 361 \\ \sqrt{Δ} = 19 \\ x_{1} = \frac{ - 17 - 19}{6} = \frac{ - 36}{6} = - 6 \\ x_{2} = \frac{ - 17 + 19}{6} = \frac{1}{3} [/tex]
[tex]2.1 { x }^{2} + 4.2x - 6 = 0 \\ Δ ≈ 17.6 - 4 \times 2.1 \times ( - 6) ≈ 17.6+ 50.4 ≈ 68 \\ \sqrt{Δ} ≈8 \\ x_{1} ≈ \frac{ - 4.2 - 8}{4.2} ≈3 \\ x_{2} ≈ \frac{ - 4.2 + 8}{4.2} ≈1[/tex]
[tex]2 {x}^{2} - x + 5 = 0 \\ Δ = 1 - 4 \times 2 \times 5 < 0[/tex]
brak miejsc zerowych
[tex]4 {x}^{2} - 4x + 1 = 0 \\ Δ = 16 - 4 \times 4 \times 1 = 0 \\ x_{0} = \frac{4}{8} = \frac{1}{2} [/tex]
[tex] \frac{1}{4} {x}^{2} + 3x + 9 = 0 \\ {x}^{2} + 12x + 36 = 0 \\ Δ = 144 - 4 \times 1 \times 36 = 144 - 144 = 0 \\ x_{0} = \frac{ - 12}{2} = - 6[/tex]
[tex]9 {x}^{2} + 6x + 1 = (3x + 1)^{2} \\ 3x + 1 = 0 \\ 3x = - 1 \\ x = - \frac{1}{3} [/tex]
