Question: If the roots of $(b - c)x^{2} + (c - a)x + (a - b) = 0$ are equal then $a + c =$...

Question

If the roots of $(b - c)x^{2} + (c - a)x + (a - b) = 0$ are equal then $a + c =$

Answer 1

$b - c + c - a + a - b = 0$

Hence one root is 1.Also as roots are equal, other root will also be equal to 1.

Also $\alpha.\beta = \frac{a - b}{b - c}$ ⇒ $1.1 = \frac{a - b}{b - c}$ ⇒ $a - b = b - c$ ⇒ $2b = a + c$

Question: If the roots of \((b - c)x^{2} + (c - a)x + (a - b) = 0\) are equal then \(a + c =\)...