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Obtain all other zeroes of 3x^{4} + 6x^{3} – 2x^{2} – 10x – 5, if two of its zeroes are `sqrt(5/3)` and - `sqrt(5/3)`

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#### Solution

p(x) = 3x^{4} + 6x^{3} – 2x^{2} – 10x – 5

Since the two zeroes are sqrt(5/3) and – sqrt(5/3).

∴ `(x-sqrt(5/3))(x+sqrt(5/3)) = (x^2-5/3)` is factor of 3x^{4}+6x^{3}-2x^{2}-10x-5

Therfore, we divide the given polynomial by x^2-5/3

we factorize x^{2}+2x+1

=(x+1)^{2}

Therefore, its zero is given by x+1=0

x = -1

As it has the term (x + 1)^{2} , therefore, there will be 2 zeroes at x = – 1.

Hence, the zeroes of the given polynomial are `sqrt(5/3)` and – `sqrt(5/3)` , – 1 and – 1

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