Question

If the roots of the equation (b − c)x

2 + (c − a)x + (a − b) = 0 are equal, show that a,b,c are in AP.

Answer 1

Step-by-step explanation:

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

therefore we can say that a,b,c are in A.P