If a, b, c are positive rational numbers such that a > b > c and the quadratic equation (a + b –2c) x 2 + (b + c –2a) x + (c + a –2b) has a root in the interval (–1, 0), then-
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(a, b, c, d)
and given equation is 
∵ Equation (ii) has a root in the interval 
From (i), 
and 
from (iii) and (iv), 
or 
. Option is correct. Again, the sum of coefficients of the equation 
that is one root is 1 and the other root is 
,
which is a rational number as 
are rational. Hence, both the roots of the equation are rational.
is correct. Further, the discriminate of equation 
is 
As deduced earlier, 
. Also, each of 
are positive.
∴ The equation 
has real and negative roots. So is also correct.
Similarly is also correct.
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