Question

. Find all the zeroes of the polynomial x4
– 5x3 + 2x2+10x-8, if two of its zeroes are 4 and 1.

Answer 1

Answer :-

since 4 and 1 are zeroes of given polynomial .

so, (x - 4)(x - 1) will be factors of polynomial .

then,

→ (x - 4)(x - 1) = x² - 5x + 4

dividing by long division method we get,

x² - 5x + 4 ) x⁴ – 5x³ + 2x² +10x - 8 ( x² - 2

x⁴ - 5x³ + 4x²

-2x² + 10x - 8

-2x² + 10x - 8

0

therefore,

→ x² - 2 = 0

→ x² = 2

→ x = ±√2

Hence, all the zeroes of the given polynomial are {√2, - √2 , 1 and 4 }

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