Question

the roots of equation (a-b+c)x^2-2cx +(b+c-a)=0 are​

Answer 1

$\huge\star{\underline{\mathfrak{Answer}}}$

Given quadratic equation is (a – b)x2 + (b – c)x + (c – a) = 0 Since the root are equal, discriminent of the quadritic equation = 0 Hence (b – c)2 = 4(a – b)(c – a) ⇒ b2 + c2 – 2bc = 4(ac – a2 – bc + ab) ⇒ b2 + c2 – 2bc = 4ac – 4a2 – 4bc + 4ab ⇒ b2 + c2 – 2bc – 4ac + 4a2 + 4bc – 4ab = 0 ⇒ b2 + c2 + 4a2 + 2bc – 4ac – 4ab = 0 ⇒ b2 + c2 + (2a)2 + 2(b)(c) – 2(2a)c – 2(2a)b = 0 ⇒ b2 + c2 + (–2a)2 + 2(b)(c) + 2(–2a)c + 2(–2a)b = 0 ⇒ (b + c – 2a)2 = 0 ⇒ b + c – 2a = 0 ∴ b + c = 2a