Question

Show that the roots of the equation
x2 + ax – b2=0 are real for all values of a and b.​

Answer 1

Step-by-step explanation:

centre of cirlce (

2

α+β

,

2

γ+δ

)→(−a,−p)

Radius of circle =

2

1

(α−β)

2

+(γ−δ)

2

=

2

1

(α+β)

2

−4αβ+(γ+δ)

2

−4γδ

=

2

1

4a

2

−4b

2

+4p

2

−4q

2

=

a

2

−b

2

+p

2

−q

2

Equation

(x+a)

2

+(y+p)

2

=a

2

−b

2

+p

2

−q

2

x

2

+y

2

+2ax+2py+b

2

+q

2

=0