Obtain all zeroes of polynomial f{x} = 3x4+6x3-2x2-10x-5. If two of its zeroes are+-underoot 5/3
Answers
Answer:
the zeros are: - √ 5/3 & √t 5/3 & -1
Step-by-step explanation:
given polynomial p(x) = 3x^4 + 6x³ - 2x² - 10x -5
given zeros are;
√5/3 and -√5/3
the factors are:
(x + √5/3) ------------------------ (1)
(x - √5/3) ------------------------- (2)
multiplying 1 and 2
x²- 5/3 --------------------------------(3)
dividing p(x) by (3)
x²-5/3 ) 3x^4 + 6x³ - 2x² - 10x - 5 ( 3x² + 6x +3
3x^4 + 0 - 5x²
------------------------------------
0 + 6x³ + 3x² - 10x
6x³ +0 - 10x
--------------------------------------
0 + 3x² - 5
3x² - 5
--------------------------------------
0 0
Quotient is : 3x² + 6x + 3
factorizing the quotient
3x² + 6x + 3
3x² + 3x + 3x + 3
3x ( x + 3 ) + 3 ( x + 1 )
( 3x + 3 ) ( x + 1 )
x = -1
the zeros are √ 5/3 & √t 5/3 & -1
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