Question

find the other zero of the polynomial x ^4 - 5 x^ 3 + 2 x^ 2 + 10 x - 8 if it is given that two of its zeros are -√2 and √2
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Answer 1

Step-by-step explanation:

(x + √2) (x - √2) = 0

x² - 2 = 0

x² - 5x + 4

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x² - 2 √ x⁴ - 5x³ + 2x² + 10x - 8 \_

-x⁴ + 2x²

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-5x³ + 4x² + 10x - 8

+5x³ - 10x

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4x² - 8

-4x² + 8

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0 0

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(x² - 5x + 4) = 0

x² - 4x - x + 4 = 0

x(x - 4) -1 (x - 4) = 0

(x - 1) (x - 4) = 0

x = 1 , 4

So , the other two zeroes are 1 & 4 .