Question

if the quadratic equation (a-b)xsqare+(b-c)x+(c-a)=0are equal ,prove that 2a=b+c​

Answer 1

For equal roots

D=0

${(b - c)}^{2} - 4(a - b)(c - a) = 0$

${b}^{2} + {c}^{2} - 2bc - 4(ac - {a}^{2} - bc + ab) = 0$

${b}^{2} + {c}^{2} - 2bc - 4ac + 4 {a}^{2} + 4bc - 4ab = 0$

Solve this.