# Obtain all other zeroes of 3x4 + 6x3 – 2x2 – 10x – 5, if two of its zeroes are and .

p(x) = 3x4 + 6x3 – 2x2 – 10x – 5

Since the two zeroes are

is a factor of 3x4 + 6x3 – 2x2 – 10x – 5

Therefore, we divide the given polynomial by

We know,
Dividend = (Divisor × quotient) + remainder

3 x4 + 6 x3 – 2x2 – 10 x – 5

3 x4 + 6 x3 – 2 x2 – 10 x – 5
As (a + b)2 = a2 + b2 + 2ab

3 x4 + 6 x3 – 2 x2 – 10 x – 5 = 3 (x + 1)2

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

Hence, the zeroes of the given polynomial are and – 1, –1.

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