Form the quadratic equation, if the roots are : (1) 0 and 7
`2-sqrt5,2+sqrt5`

Answer

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

Explanation

Let `alpha=2-sqrt5andbeta=2+sqrt5`
Then `alpha+beta=2-sqrt5+2+sqrt5=4andalphabeta=(2-sqrt5)(2+sqrt5)=(2)^(2)-(sqrt5)^(2)`
=4-5=-1
Then required quadratic equation is
`x^(2)-(alpha+beta)x+alphabeta=0`
i.e. `x^(2)-4x+(-1)=0`
i.e. `x^(2)-4x+(-1)=0`