Question

Ajutatimaa va rog e urgent

Answer 1

Răspuns:

Explicație pas cu pas:

a) x²-10x+21 = x²-3x-7x+21 = x(x-3)-7(x-3) = (x-3)(x-7)

Δ = 100-84 = 16 => √Δ = 4  => x₁,₂ = (10±4)/2 => x₁ = 6/2 = 3 ; x₂ = 14/2 = 7

=> x²-10x+21 = (x-x₁)(x-x₂) = (x-3)(x-7)

b) 6x²-11x+3 = 6x²-9x-2x+3 = 3x(2x-3)-(2x-3 = (2x-3)(3x-1)

Δ = 121-72 = 49 => √Δ = 7 => x₁,₂ = (11±7)/12 => x₁ = 4/12 = 1/3 ; x₂ = 18/12=3/2

6x²-11x+3 = (3x-1)(2x-3)

c) 3x²+7x-6 = 3x²+9x-2x-6 = 3x(x+3)-2(x+3) = (x+3)(3x-2)

Δ=49+72 = 121 => √Δ=11 => x₁,₂=(-7±11)/6 => x₁ = -3 ; x₂ = 2/3=>

3x²+7x-6 =(x+3)(3x-2)

d) -2x²+3x+2= -2x²+4x-x+2 = 2x(-x+2) + (-x+2) = (-x+2)(2x+1)

Δ=9+16=25 => √Δ=5 =>x ₁,₂=(-3±5)/-4 => x₁= 2 ; x₂= -1/2

-2x²+3x+2= (x-2)(-2x-1) = (2-x)(2x+1)

e) 4x²+x+1 = nu se descompune   Δ = 1-16 < 0

f) 2x²+4x-5 = 0   =>

x₁,₂ = [-4±√(16+40)]/4 = [-4±√56]/4 = (-4±2√14)/4 = (-2±√14)/2

x₁ = (-2-√14)/2  ; x₂ = (-2+√14)/2

2x²+4x-5 = [x-(-2-√14)/2]·[x-(-2+√14)/2]