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Question
Find the zeroes of the polynomial f(x) = `2sqrt3x^2-5x+sqrt3` and verify the relation between its zeroes and coefficients.
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Solution
`2sqrt3x^2-5x+sqrt3`
`2sqrt3x^2-2x-3x+sqrt3`
`2x(sqrt3x-1) or (2x-sqrt3=)=0`
`(sqrt3x-1)=0 or (2x-sqrt3)=0`
`x=1/sqrt3 or x=sqrt3/2`
`x=1/sqrt3xxsqrt3/sqrt3=sqrt3/3 or x=sqrt3/2`
Sum of zeroes= `sqrt3/3+sqrt2=(5sqrt3)/6 = -(("coefficient of" x))/(("coefficient of" x^2))`
Product of zeroes=`sqrt3/3xxsqrt3/2=sqrt3/6= ("constant term")/(("coefficient of "x^2))`
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