Question

if b-c multiplied by x2 plus c minus a multiplied by x plus a minus b=0 prove 2b=a plus c ​

Answer 1

Answer:

(b-c)x²+(c-a)x +a-b=0

=> (b-c)x²-(b-c)x- (a-b)x +(a-b)=0

=> (b-c)x( x-1) -(a-b)(x-1)= 0

=> (x-1) [ (b-c)x-(a-b)]=0

=> x= 1 and x= (a-b)/(b-c)

comparing the values of x

=> (a-b)/(b-c) = 1

=> a-b= b-c

=> 2b = a+c

proved

I hope this is helpful for you

note=> this is true only when both

the roots of this quadratic equation

are identical ( equal).