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# Solve:

Asked by Anish 4th September 2018, 10:45 PM
a1x2 + b1 x + c1 = 0 and a2x2 + b2 x + c2 = 0 have common root.
The condition of common root of the both quadratic equation is
(a2 c1 - a1 c2)2 = (b1 c2 - b2 c1)(a1 b2 - a2 b1)........(i)
According to the given quadratic equations,
a1 = a, a2 = a', b1 = 2b, b2 = -2b', c1 = c and c2 = c'
Hence,
(a2 c1 - a1 c2)2 = 4(b1 c2 + b2 c1)(a1 b2 + a2 b1)..........(ii)
The condition of equal roots is b2 - 4ac = 0.....(iii)
(b12 - a1 c1)x2 + (2b1 b2 - a1 c2 - a2 c1)x + (b22 - a2 c2) = 0 has equal roots.
using (iii)
(2b1 b2 - a1 c2 - a2 c1)2 = 4(b12 - a1 c1)(b22 - ac2).......(iv)
Expand (ii) and reaaranging you will get equation (iv).
Hence, (b2 - 4ac)x2 + (2bb' - ac' - a'c)x + (b'2 - a'c') = 0 has equal roots.

Answered by Expert 14th September 2018, 9:30 AM
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