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Question
Find the zeroes of the following quadratic polynomials and verify the relationship between the zeroes and the coefficients
`f(x)=x^2-(sqrt3+1)x+sqrt3`
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Solution
`f(x)=x^2-(sqrt3+1)x+sqrt3=x^2-sqrt3-x+sqrt3`
`=x(x-sqrt3)-1(x_sqrt3)`
`=(x-1)(x-sqrt3)`
Zeroes of the polynomials are 1 and `sqrt3`
Sum of zeroes `="-(coefficient of x)"/("coefficient of "x^2)=(-(-sqrt3-1))/1`
`1+sqrt3=sqrt3+1`
Product of zeroes `="constant term"/"coefficient of"x^2=sqrt3/1`
`1xxsqrt3=sqrt3`
`sqrt3=sqrt3`
Hence, relationship verified
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