Question

show (a-b+c)x2+4(a-b)x+4(a-b)x+(a-b-c)=0 has real roots​

Answer 1

Answer:

If discriminant is a perfect square then roots are rational.

D=b

2

−4ac

D=(2c)

2

−4(a+c−b)(b+c−a)

D=4c

2

−4[ab+ac−a

2

+bc+c

2

−ac−b

2

−bc+ab]

D=4c

2

−4[−a

2

−b

2

+c

2

+2ab]

D=4c

2

−4c

2

+4(a

2

+b

2

−2ab)

D=4(a−b)

2

D=(2(a−b))

2

D is perfect square of 2(a−b)

Hence roots are rational.