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The other zeroes of $3 x 4 + 6 x 3 − 2 x 2 − 10 x − 5,$ if two of its zeroes are $53$ and $− 53$ are:

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-1, -5

-1, -1

-1, 5

-1, 8

answer is B.

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Detailed Solution

Given a polynomial

3 x 4 + 6 x 3 − 2 x 2 − 10 x − 5

.
As,

x = 53

and

x = − 53

are the zeros of polynomial.
Therefore,

x + 53 x − 53

are the factors of the given polynomial.

= x 2 − 532

= x 2 − 53 3 x 2 − 5 = 0

Using a long division method, dividing the polynomial,
Question Image

So, the quotient is,

x 2 + 2 x + 1 = 0 (x 2 + x) + (x + 1) = 0 x (x + 1) + 1 (x + 1) = 0 (x + 1) (x + 1) = 0

x = -1, -1.
Hence, the 4 zeros are

53, − 53, − 1, − 1

.
Therefore, option 2 is correct.

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