Question

if the roots of the equation (a-b)x^2+(b-c)x+c-a=0are equal .prove that 2a=b+c

Answer 1

if roots are equal then discriminant of equation should be zero
$d = \sqrt{(b - c) {}^{2} - 4(a - b)(c - a)} = 0 \\ (b - c) {}^{2} = 4(a - b)(c - a) \\ {b}^{2} + c {}^{2} - 2bc = 4ac - 4 {a }^{2} \\ - 4 {bc} + 4ab \\ \\ (2a - b - c) {}^{2} = 0 \\ 2a = b + c$

mark as brainliest if helped