Question

slove this question

Answer 1

We know that.,,

If the quadratic equation ax^2+bx+c=0, whose roots are equal then its determinant is equal to 0.

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

Determinant =0,,

Now

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

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

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

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

> b+c-2a=0

therefore,,,

b+c=2a

So,,, 2a=b+c

Proved..........