1.

If the roots of the equation (b - c)x2 + (c - a) x + (a - b) = 0 are equal, then prove that 2b = a + c.

Answer»

If the roots of the given equation are equal, then discriminant is zero i.e.

(c - a)2 - 4(b - c) (a - b) = 0 

=> c2 + a2 - 2ac + 4b2 - 4ab + 4ac - 4bc = 0

=>c2 + a2 + 4b2 + 2ac - 4ab - 4bc = 0

=>(c + a - 2b)2 = 0

=>c + a = 2b Hence Proved.



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