Question

if the roots of the quadratic eqation (a-b)x^2+(b-c)x+(c-a)=0 are equal then prove that 2a=b+c​

Answer 1

Answer:

b+c=2a

Step-by-step explanation:

b²-4ac=0

(b-c)²-4(a-b)(c-a)=0

b²+c²-2bc-4(ac-a²-bc+ab)

b²+c²-2bc-4ac+4a²+4bc-4ab=0

4a²+b²+c²-4ab+4bc-4ac=0

(2a)²+b²+c²-4ab+4bc-4ac=0

(-2a+b+c)²=0.............(a+b+c)²=a²+b²+c²+2ab+2bc+2ca

-2a+b+c=0...................rooting on both sides

b+c=2a