Find all the zeroes of the polynomial p (x) = x4 - 7x³ + 9x² + 13x - 4, if two of its zeroes are (2 + √ 3) and (2 - √ 3).

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Mathematics

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8 February, 17:00

Find all the zeroes of the polynomial p (x) = x4 - 7x³ + 9x² + 13x - 4, if two of its zeroes are (2 + √ 3) and (2 - √ 3).

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Answers (1)

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Howard Lozano · Answer 1

Polynomial of the two zeroes

(x - (2+rt (3)) (x - (2-rt (3)) = x^2 - 4x + 1

divide it

(x^4 - 7x^3 + 9x^2 + 13x - 4) / (x^2 - 4x + 1)

= x^2 - 3x - 4

= (x-4) (x+1)

x=-1, 4 ... the remaining zeroes