Rozwiąż równania. a) [latex]5 x^{2}+2 x^{4}+ x^{3}=0 [/latex] b) [latex]-2 x^{3}-6 x^{2}+8x=0 [/latex] c) [latex] x^{5} -7 x^{4} +12 x^{3} =0[/latex] d) [latex]20 x^{6}+ x^{5}= x^{4} [/latex] Proszę o dokładne rozwiązania. Dziękuję.

[latex]a)\5 x^{2} +2x^{4} + x^{3} = 0\\ x^{2} (2 x^{2} +x+5) = 0\\ x^{2} = 0 => x = 0\\lub\\2 x^{2} +x+5) = 0\\Delta = b^{2} - 4ac = 1 - 40 = -39 < 0\\x = 0[/latex] [latex]b)\-2x^{3} - 6 x^{2} + 8x = 0\\-2x( x^{2} + 3x - 4) = 0\\-2 x^{2} = 0 => x = 0\\lub\\ x^{2} +3x-4 = 0\\Delta = 9 + 16 = 25\\sqrt{Delta} = 5\\x_1 = frac{-3-5}{2} = -4\\x_2 = frac{-3+5}{2} = 1\\x = -4 V x = 0 V x = 1[/latex] [latex]c)\x^{5} - 7x^{4} + 12x^{3} = 0\\x^{3}( x^{2} -7x+12) = 0\\x^{3} = 0 => x = 0\\lub\\ x^{2} -7x+12 = 0\\Delta = 49-48 = 1\\sqrt{Delta} = 1\\x_1 = frac{7-1}{2} = 3\\x_2 = frac{7+1}{2} = 4\\x = 0 V x = 3 V x = 4[/latex] [latex]d)\20x^{6} + x^{5} = x^{4}\\20x^{6} + x^{5} - x^{4} = 0\\x^{4}(20 x^{2} + x - 1) = 0\\x^{4} = 0 => x = 0\\lub\\20 x^{2} +x-1 = 0\\Delta = 1 + 80 = 81\\sqrt{Delta} = 9\\x_1 = frac{-1-9}{40} = -frac{1}{4}\\x_2 = frac{-1+9}{40} = frac{1}{5}\\x = -frac{1}{4} V x = 0 V x = frac{1}{5}[/latex]

a) 5x^2 + 2x^4 + x^3 = 0 x^2(2x^2 + x +5) = 0 x^2=0 v 2x^2 + x +5=0 <-- sprzeczne x = 0 odp. x=0 b) -2x^3 -6x^2 +8x = 0 -2x(x^2 +3x -4)=0 -2x(x^2+4x - x -4 )=0 -2x ( x(x+4)-(x+4))=0 -2x(x+4)(x-1)=0 x=0 v x=-4 v x=1 odp. x€{ -4,0,1} c) x^5 -7x^4 +12x^3 = 0 x^3 ( x^2 - 7x +12)=0 x^3(x^2-3x-4x +12)=0 x^3(x(x-3)-4(x-3))=0 x^3(x-3)(x-4)=0 x=0 v x=3 v x=4 odp. x€{ 0,3,4} d) 20x^6 + x^5 - x^4 = 0 x^4(20x^2 + x -1)=0 x^4=0 x=0 v 20x^2 + x - 1 = 0 delta =1+80=81 pierw. z delta=9 x1=(-1-9)/40=-1/4 x2=(-1+9)/40=1/5 odp. x€{ -1/4, 0 , 1/5}