AP EAPCET 24-Aug-2021 Shift 1 Paper

Equation x2−ax+b and x2+bx−a have a common root. Let alpha be the common root of both quadratic equations
⇒α2−aα+b=0
α2+bα−a=0
Using cross-multiplication

α2

−a b b −a

=

α

b 1 −a 1

=

1

1 −a 1 b

α2

a2−b2

=

α

b+a

=

1

b+a

We get

α

b+a

=

1

b+a

⇒α=1
Now, using first two fraction

1

a2−b2

=

1

a+b

⇒a+b=a2−b2
⇒(a+b)=(a+b)(a−b)
⇒(a+b)(a−b−1)=0
a+b=0 or a−b−1=0
⇒a−b=1