Question

Obtain all zeros of the polynomial f(x) = x⁴ – 3x³ – x² + 9x – 6 if two of its zeros are –√3 and √3 .​

Answer 1

We know that if x = a is a zero of a polynomial then x – α is a factor of f(x). Since –√3 & √3 are zeroes of f(x). Therefore ( x + √3 ) and ( x – √3 ) are factors of f(x).

Now on dividing.

f(x) = x⁴ – 3x³ – x² + 9x –6 by g(x)=(x – √3)(x + √3)

to find other zeroes.

___________________

x²–3 ) x⁴ – 3x³ – x² + 9x –6 ( x²– 3x + 2

x⁴ – 3x²

– +

____________________

– 3x³ + 2x² + 9x – 6

– 3x³ + 9x

+ —

____________________

+ 2x² — 6

2x² — 6

— +

_____________________

0

By applying division algorithm, we have :

x⁴-3x³-x²+9x-6 = (x-√3)(x+√3)(x²–3x+2)

x⁴-3x³-x²+9x-6 = (x-√3)(x+√3)(x²–2x–x+2) x⁴-3x³-x²+9x-6 = (x-√3)(x+√3)(x-2)(x-1)

Hence, the zeroes of the polynomial are : √3,-√3, 1 &2..

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Answer 2

Answer:

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Step-by-step explanation:

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