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kvadratické rovnice bez absolutního členu
kvadratická rovnice bez lineárního členu
kvadratická rovnice (Vietovy vztahy)
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lin. nerovnice
100

x² - 6x = 0

x₁ = 0, x₂ = 6

100

x² - 25 = 0

x₁ = 5, x₂ = -5

100

x² - 7x + 10 = 0

x₁ = 2, x₂ = 5

100

3x - 7 = 11

x = 6

100

2x - 5 > 3

x > 4, tj. x ∈ (4, ∞)

200

3x² + 12x = 0

x₁ = 0, x₂ = -4

200

3x² - 48 = 0

x₁ = 4, x₂ = -4

200

x² + 3x - 18 = 0

x₁ = 3, x₂ = -6

200

5x + 4 = 2x - 5

x = -3

200

4 - 3x ≤ 10

x ≥ -2, tj. x ∈ <-2, ∞)

300

5x² - 7x = 0

x₁ = 0, x₂ = 7/5 = 1,4

300

2x² + 18 = 0

Nemá řešení v R

300

x² - x - 20 = 0

x₁ = 5, x₂ = -4

300

4(x - 2) = 2(x + 5)

x = 9

300

(x - 1)/3 ≥ (x + 2)/2

x ≤ -8, tj. x ∈ (-∞, -8>

400

2x(x - 4) = x² - 3x

x₁ = 0, x₂ = 5

400

4x² - 27 = 0

x = ± (3√3)/2

400

x² + 8x + 12 = 0

x₁ = -2, x₂ = -6

400

(x + 2)/3 = (x - 1)/2

x = 7

400

(x² - 9) / (x² - 4) ≤ 0

x ∈ <-3, -2) ∪ (2, 3>

500

3x(x - 2) = (x - 2)(x + 2) + 4

x₁ = 0, x₂ = 3

500

(x + 3)(x - 3) = 2x² - 25

x₁ = 4, x₂ = -4

500

x² + px + q = 0, je-li x₁ = -5 a x₂ = 3

x² + 2x - 15 = 0

500

(2x - 1)/4 - (x - 3)/2 = 2

Nemá řešení (5 = 8)

500

(x² - 2x - 15) / (x² - 1) ≤ 0

x ∈ <-3, -1) ∪ (1, 5>