Question

Find zeros of polynomial `x^2-5` and verify the relationship between zero and coefficients.

Answer 1

`x^2-5=0`
`x=pmsqrt5`
`x=sqrt5,-sqrt5`
`x^2+(alpha+beta)x+alphabeta=0`
`alpha+beta=sqrt5-sqrt5=0`
`alpha*beta=sqrt5*sqrt5=-5`
`x^2+0x+(-5)=0`
`x^2`+(sum of roots)x+(product of roots)=0.