Q. 54.3( 26 Votes )

If the roots of t

Answer :

When we compare the above quadratic equation with the generalized one we get,

ax2 + bx + c = 0


a = b – c


b = c – a


c = a – b


Since the quadratic equations have real and equal roots,


b2 – 4ac = 0 for real and equal roots


(c – a) 2 – [4 × (b – c) × (a – b)] = 0


c2 – 2ac + a2 – [4 × (ba – b2 – ca – bc)] = 0


c2 – 2ac + a2 – [4ba – 4b2 – 4ca + 4bc] = 0


c2 – 2ac + a2 4ba + 4b2 + 4ca - 4bc = 0


c2 + a2 4ba + 4b2 + 2ac - 4bc = 0


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


a2 + (-2b)2 + c2 + 2 × a(-2b) + 2 × (-2b)c + 2 × ac = 0


We have the following formula:


(a + b + c)2 = a2 + b2 + c2 + 2ab + 2bc + 2ac


So according to the formula


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


Taking square root of both sides


a + (-2b) + c = 0


2b = a + c


Hence Proved.


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