Obtain all the zeros of x^4+6x^3+x^2-24x-30 if 2 zeros are 2 and -5

1.	Obtain all the zeros of x^4+6x^3+x^2-24x-30 if 2 zeros are 2 and -5
Answer» As x = 2 and -5 are the zeroes of x4 + 6x3 + x2- 24x - 20.{tex}\\Rightarrow{/tex}\xa0(x - 2) and (x + 5) are two factors of x4 + 6x3 + x2\xa0-24x - 20{tex}\\Rightarrow{/tex}\xa0product of factors is (x - 2) (x + 5) = x2 + 3x - 10Dividing x{tex}^4{/tex} + 6{tex}x^3{/tex}+\xa0{tex}x^2{/tex} - 24x - 20 by\xa0{tex}x^2{/tex} + 3x - 10Dividend = divisor {tex}\\times{/tex}\xa0quotient + remainder{tex}\\Rightarrow{/tex}\xa0x4 + 6x3 + x2 - 24x - 20 = (x2 + 3x -10) (x2 + 3x + 2)= (x - 2) (x + 5) (x + 2) (x + 1)Hence, other two zeroes are -2 and -1.

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