Question

if the roots of the quadratic equations (a-b)xsquare+(b-c)x+(c-a)=0 are equal then prove that 2a=a+c

Answer 1

$\huge\mathfrak{Question}$

if the roots of the quadratic equations (a-b)xsquare+(b-c)x+(c-a)=0 are equal then prove that 2a=a+c

$\huge\mathfrak{Answer}$

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Answer 2

if the roots of the quadratic equations (a-b)xsquare+(b-c)x+(c-a)=0 are equal then prove that 2a=a+c

,,

comparing above with quadratic equations, we get

a=(a-b)

b=(b-c)

c=(c-a)

since roots are equal

b^2=4ac

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

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

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

b^2

I think there is something mistake in the question