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Question

Obtain all the zeros of 3x4+6x32x210x5, if two of its zeros are 53 and 53

A
Zeros are 53,53,1 and 1.
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B
Zeros are 53,53,1 and 0.
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C
Zeros are 53,53,1 and 0.
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D
Zeros are 53,53,1 and -1.
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Solution

The correct option is D Zeros are 53,53,1 and -1.
f(x)=3x4+6x22x210x5
Given,  53 and  53 are the zeros of f(x).
x 53(x+53) are the factors of f(x).
(x253) are the factor of f(x) or (3x25) are the factor of f(x).
So, 3x4+6x32x210x5
=(3x25)(x2+2x+1)
=3(x253)(x+1)2
=3x 53x+ 53(x+1)2
Zeros are  53, 53,1 and 1.

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