Rozwiązane

Mega potrzebuje na dziś rozwiązań tych zadań ! daje naj



Mega Potrzebuje Na Dziś Rozwiązań Tych Zadań Daje Naj class=

Odpowiedź :

Kontonawszystko

Odpowiedź:

zad. 4

[tex]w(x) = 2 {x}^{3} + 4 {x}^{2} + 2x = 2x( {x}^{2} + 2x + 1) = 2x(x + 1 {)}^{2} [/tex]

[tex]w(x) = 25 {x}^{3} - x = x(25 {x}^{2} - 1) = x(5x - 1)(5x + 1)[/tex]

zad. 5

[tex] {x}^{5} - 7 {x}^{4} + 12 {x}^{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 - 4)(x - 3) = 0 \\ x_{1} = 0 \: \: \: \: \: x_{2} = 4 \: \: \: \: \: x_{3} = 3[/tex]

Basetla

4.

[tex]w(x) = 2x^{3}+4x^{2}+2x=2x(x^{2}+2x+1) = 2x(x+1)^{2} = 2x(x+1)(x+1)\\\\w(x) = 25x^{3}-x = x(25x^{2}-1) = x(5+1)(5-1)[/tex]

5.

[tex]x^{5}-7x^{4}+12x^{3} = 0\\\\x^{3}(x^{2}-7x+12) = 0\\\\x_{o} = 0\\\\lub\\\\x^{2}-7x+12 = 0\\\\a = 1, \ b = -7, \ c = 12\\\\\Delta = b^{2}-4ac = (-7)^{2}-4\cdot1\cdot12 = 49-48 = 1\\\\\sqrt{\Delta} = \sqrt{1} = 1\\\\x_1 = \frac{-b-\sqrt{\Delta}}{2a} = \frac{-(-7)-1}{2\cdot1} = \frac{6}{2} = 3\\\\x_2 = \frac{-b+\sqrt{\Delta}}{2a} = \frac{7+1}{2} = \frac{8}{2} = 4\\\\x \in \{0, 3, 4\}[/tex]

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