Question

(b-c)x^2+(c-a)X+(a-b)=0​

Answer 1

Answer:Step-by-step explanation:If roots of a quadratic equation are equal, then discriminant of the quadratic equation is 0

D=b  

2

−4ac=0

(b−c)x  

2

+(c−a)x+(a−b)=0

Comparing with  

ax  

2

+bx+c=0

Here, a=(b−c), b=(c−a) and c=(a−b)

So,

⇒(c−a)  

2

−4(b−c)(a−b)=0

⇒c  

2

+a  

2

−2ac−4(ab−b  

2

−ac+bc)=0

⇒c  

2

+a  

2

−2ac−4ab+4b  

2

+4ac−4bc=0

⇒c  

2

+a  

2

+2ac+4b  

2

−4ab−4bc=0

⇒(c+a)  

2

+4b  

2

−4b(a+c)=0

⇒(c+a)  

2

+(2b)  

2

−2(c+a)(2b)=0

⇒[(c+a)−(2b)]  

2

=0

⇒c+a−2b=0

⇒2b=c+a