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`

 

Answer 1

`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