Question

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

Answer 1

plz refer to this attachment

Answer 2

Hello,

Hello, AKASHITEMHEAVEN HERE,

The question must be, if roots of equation (a-b)x2+(b-c)x+(c-a)=0 are equal , prove that b+c = 2a.

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

Hence proved.

Hope it helps you

Thanks