g) [latex]5x^5 + 2x^4 + 10x^3 + 4x^2 = x^4(5x + 2) + 2x^2(5x + 2) = x^2(5x + 2)(x^2 + 2)[/latex] h) [latex]-4x^4+ 5x^3 + 12x -15 = -x^3(4x - 5) + 3(4x - 5) = (4x - 5)(3 - x^3) = (4x - 5)(sqrt[3]{3} - x)(x^2 + xsqrt[3]{3} + sqrt[3]{9})[/latex] a) [latex](2x-3)(x+5)=(5x+9)(6+3x)\ 2x^2 - 3x + 10x - 15 = 30x + 36 + 27x + 15x^2\ 13x^2 + 50x + 51 = 0\ Delta = 50*50 - 52*51 < 0[/latex] b) [latex]x(2x+7)-5=(x+4)(5-x)\ 2x^2 + 7x - 5 = - x^2 + 20 - 4x + 5x\ 3x^2 + 6x - 25 = 0\ Delta = 36 + 9*25 = 9(4 + 25)\ x = frac{-3 + 3sqrt{29}}{6} = frac{-1 + sqrt{29}}{2} vee x = frac{-3 - 3sqrt{29}}{6} = - frac{1 + sqrt{29}}{2}[/latex] c) [latex](3x-1)(2-x)-x(x+3)=2 \ 6x - 3x^2 - 2 + x - x^2 - 3x = 2\ 4x^2 - 4x + 4 = 0\ x^2 - x + 1 = 0\ Delta = 1 - 4 < 0[/latex]
g) 5x⁵ + 2x⁴+ 10x³ +4x² 5x³(x²+2)+2x²(x²+2) (5x³+2x²)(x²+2) x(5x²+2x)(x²+2) h) -4x⁴+ 5x³ + 12x -15 -4x(x³-3)+5(x³-3) (-4x+5)(x³-3) i nie wiem co z tym sześcianem a) -13x²-50x-69=0 Δ=b²-4ac Δ=2500-3588=-1088 Δ<0 sprzeczny b) x(2x+7)-5=(x+4)(5-x) 2x²+7x-5=5x-x²+20-4x 2x²+x²+7x-5x+4x-5-20=0 3x²+6x-25=0 Δ=b²-4ac Δ=36+300=336 [latex]sqrtDelta=sqrt336=sqrt{16*21}=4sqrt{21}[/latex] [latex]x_1=frac{-b-sqrtDelta}{2a}=frac{-6-4sqrt{21}}{6}=frac{2(-3-2sqrt{21})}{6}=frac{-3-2sqrt{21}}{3}[/latex] [latex]x_2=frac{-b+sqrtDelta}{2a}=frac{-6+4sqrt{21}}{6}}=frac{2(-3+2sqrt{21})}{6}=frac{-3+2sqrt{21}}{3}[/latex] c) (3x-1)(2-x)-x(x+3)=2 6x-3x²-2+x-x²+3x-2=0 -4x²+10x-4=0 Δ=b²-4ac Δ=100-64=36 [latex]x_1=frac{-b-sqrtDelta}{2a}=frac{-10-6}{-8}=frac{-16}{-8}=2 [/latex] [latex]x_2=frac{-b+sqrtDelta}{2a}=frac{-10+6}{-8}}=frac{-4}{-8}=frac{1}{2}[/latex] ale sprawdź w wynikach czy się zgadza
