Question

Obtain all other zeros of 3x⁴+ 6x³- 2x²- 10x- 5, if two of its zeros are√5/3 and -√5/3​

Answer 1

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♠ Obtain all other zeros of 3x⁴+ 6x³- 2x²- 10x- 5, if two of its zeros are√5/3 and -√5/3 .

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✒ The zeroes of the given polynomial are -√(5/3), √(5/3) , -1, -1 .

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Given p(x) = 3x⁴+6x³-2x²-10x-5--(1)

The degree of p(x) is 4 , so it has

atmost 4 zeroes.

The two zeroes of given p(x) are

√(5/3) and -√(5/3)

The equation of the polynomial

whose zeroes are √(5/3) and -√(5/3 )

= ( x+√5/3 )( x - √5/3 )

= x² - 5/3 --- (2)

Divide (1) with ( 2 ) , we get

x²-5/3)3x⁴+6x³-2x²-10x-5(3x²+6x+3

********3x⁴+ 0 - 5x²

___________________

*************6x³+3x²-10x-5

*************6x³ + 0 - 10x

___________________

******************3x² + 0 - 5

******************3x² + 0 - 5

____________________

******************* ( 0 )

p(x) = ( x²-5/3)( 3x²+6x+3 )

= 3(x²-5/3)( x²+2x+1 )

= 3[ x² - {√(5/3)}² ] ( x + 1 )²

= 3(x+√5/3)(x-√5/3)(x+1)(x+1)

Therefore , The zeroes of the given polynomial are -√(5/3), √(5/3) , -1, -1 .

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Answer 2

Answer:

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