Question

m) x² + 4x + 5 = 0; n) x² - 7x - 30 = 0; o) 2x²-x-6 = 0; p) 2x² - 7x + 3 = 0; r) x² - 2x + 11 = 0.​

Answer 1

Răspuns:

Explicație pas cu pas:

m) x² + 4x + 5 = 0 =>

a = 1 ; b = 4 ; c = 5 ; Δ = b²-4ac = 4²-4·1·5 = 16-20 = -4

√Δ = √(-4) = 2i  ;

x₁,₂ = (-b±√Δ)/2a = (-4±2i)/2 = -2±i

x₁ = -2-i ; x₂ = -2+i

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n) x² - 7x - 30 = 0 =>

a = 1 ; b = -7 ; c = -30

Δ = (-7)²-4·1·(-30) = 49+120 = 169

√Δ = √169 = 13=>

x₁,₂ = (7±13)/2 => x₁ = (7-13)/2 = -3

x₂ = (7+13)/2 = 10

x₁ = -3 ; x₂ = 10

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o) 2x²-x-6 = 0 =>

a = 2 ; b = -1 ; c = -6

Δ = (-1)²-4·2·(-6) = 1+48 = 49

√Δ = √49 = 7 =>

x₁,₂ = (1±7)/2 => x₁ = -3 ; x₂ = 4

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p) 2x² - 7x + 3 = 0 =>

a = 2 ; b = -7 ; c = 3

Δ = (-7)²-4·2·3 = 49-24 = 25

√Δ = √25 = 5 =>

x₁,₂ = (7±5)/2 => x₁ = 1 ; x₂ = 6

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r) x² - 2x + 11 = 0 =>

a = 1 ; b = -2 ; c = 11

Δ = (-2)²-4·1·11 = 4-44 = -40

√Δ = √(-40) = 2i√5

x₁,₂ = (2±2i√5)/2 = 1±i√5

x₁ = 1-i√5

x₂ = 1+i√5