Question

If the roots of the Quadratic equation (a-b) x square + (b-c) x +(c-a) = 0 are equal, then prove that 2a=b+c​

Answer 1

Using Discriminant,

D = B2-4AC as compared with the general quadratic equation Ax2+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

b2+c2-2bc -4(ac-a2-bc+ab) =0

b2+c2-2bc -4ac+4a2+4bc-4ab=0

4a2+b2+c2+2bc-4ab-4ac=0

(2a-b-c)2=0

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

2a= b+c

Answer 2

Answer:

Step-by-step explanation:

Using discriminant rule as root are equal so b2-4ac =0 after solving we get 2a=b+c