Q. 204.1( 22 Votes )

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

Answer :

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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