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Verify that 3,-1,-1/3 are the zeros of t...

Verify that 3,-1,-1/3 are the zeros of the cubic polynomial `p(x)=3x^3-5x^2-11x-3`. verify the relationship between the zeros and its coefficients.

Text Solution

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`F(x)=(x-3)(x+1)(x+1/3)`
`=(x^2-3x+x-3)(x+1/3)`
`=(x^2-2x-3)(x+1/3)`
`=x^3-2x^2-3x+1/3x^2-2/3x-1`
`F(x)=x^3-5/3x^2-11/3x-1`
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