Question

If the roots of (b-c) x²+(c - a)x + (a - b) = 0 are equal, then a + c = ?

GM​

Answer 1

Answer:

a= b-c

b= c-a

c=a-b

∆=b^-4ac

∆=(c-a)^2-4×(b-c)×(a-b)

∆=c^2+a^2-2ac-4×ab-b^2-ca+cb

∆=a^2+4b^2+c^2-2ac-4ab+4ac-4cb

∆=a^2+4b^2+c^2-4ab+2ac-4cb

∆=(a-2b+c) ^2

∆=0(roots are real

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

square root on both sides

0=a-2b+c

2b=a+c