1.

Find the zeroes of the polynomial `x^2-3`and verify the relationship between the zeroes and the coefficients.

Answer» `P(x)=x^2-3`
`x^2-3=0`
`(x)^2-(sqrt3)^2`
`(x-sqrt3)(x+sqrt3)=0`
`x=sqrt3,-sqrt3`
`alpha=sqrt3,beta=-sqrt3`
`alpha+beta=sqrt3-sqrt3=0`
`alpha*beta=sqrt3(-sqrt3)=-3`
`ax^2+bx+c=0`
`alpha+beta=-b/a=-(0)/1=0`
`alpha*beta=c/a=(-3)/1=-3`


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