x^4 - 7x^2 + 4x + 20 = 0 (^ - степень). Created by MSXL. algebra-ru

x^4 - 7x^2 + 4x + 20 = 0 (^ - степень)...

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August 2022 1 0 Report

x^4 - 7x^2 + 4x + 20 = 0
(^ - степень)

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sedinalana

Verified answer

Проверим делитель числа 20 х=-2
(-2)^4-7*(-2)²+4(-2)+20=16-28-8+20=0
x^4-7x²+4x+20 |x+2
x^4+2x³ x³-2x²-3x+10
---------------
-2x³-7x²
-2x³-4x²
---------------
-3x²+4x
-3x²-6x
------------------
10x+20
10x+20
-------------
0
Получили (x+2)(x³-2x²-3x+10)=0
Проверим делитель числа 10 х=-2
(-2)³-2*(-2)²-3*(-2)+10=-8-8+6+10=0
x³-2x²-3x+10 |x+2
x³+2x² x²-4x+5
-------------
-4x²-3x
-4x²-8x
----------------
5x+10
5x+10
-----------
0
Получили (x+2)²(x²-4x+5)=0
x²-4x+5=0
D=16-20=-4<0 нет решения
Ответ х=-2

2 votes Thanks 0

Answers & Comments

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