Form the quadratic equation, if the roots are : (1) 0 and 6
`(1)/(2),-(1)/(2)`

Answer

`x^(2)-(1)/(4)=0` is the required quadratic equation

Explanation

Let `alpha=(1)/(2)andbeta=-(1)/(2)`
Then `alpha+beta=(1)/(2)+(-(1)/(2))=(1)/(2)-(1)/(2)=0`
and `alphabeta=(1)/(2)xx(-(1)/(2))=-(1)/(2)`
The required quadratic equation is
`x^(2)-(alpha+beta)x+alphabeta=0`
i.e. `x^(2)-(0)x+(-(1)/(4))=0`
i.e. `x^(2)-(1)/(4)=0`