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प्रश्न
Obtain all other zeroes of 3x4 + 6x3 – 2x2 – 10x – 5, if two of its zeroes are `sqrt(5/3)` and - `sqrt(5/3)`
उत्तर
p(x) = 3x4 + 6x3 – 2x2 – 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 3x4+6x3-2x2-10x-5
Therfore, we divide the given polynomial by x^2-5/3
we factorize x2+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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