Find all the zeroes of the polynomial p (x) = 2x^4+x^3 - 14x^2-19 x-6 If two of its zeroes are - 2 and - 1.

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Mathematics

Houdini

24 June, 12:13

Find all the zeroes of the polynomial p (x) = 2x^4+x^3 - 14x^2-19 x-6 If two of its zeroes are - 2 and - 1.

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Brennen Robertson · Answer 1

As 2 zeroes are 2 and 1 the polynomial is divisible by (x + 2) and (x + 1)

and by x^2 + 3x + 2

if we do long division the quotient is 2x^2 - 5x - 3

this factors to (2x + 1) (x - 3)

so the other zeroes are - 1/2 and 3.