Question

If the roots of the quadratic equation (a-b)x2 + (b-c)x + (c-a) = 0 are equal, prove that 2a = b+c.

Answer 1

Answer:

If the quadratic equation=ax²+bx+c=0 whose roots are equal then it's deteminant is equal to zero. Hence proved

Answer 2

$answer$

D = B^2-4AC as compared with the general quadratic equation Ax^2+Bx+C=0

so, A = a-b

B = b-c

C = c-a

For roots to be equal, D=0

(b-c)^2 - 4(a-b)(c-a) =0

b^2+c^2-2bc -4(ac-a^2-bc+ab) =0

b2+c2-2bc -4ac+4a^2+4bc-4ab=0

4a^2+b^2+c^2+2bc-4ab-4ac=0

(2a-b-c)^2=0

i.e. 2a-b-c =0

2a= b+c