The roots of the equation (b+c)x2−(a+b+c)x+a=0, where a,b,c∈Q and b+c≠a, are
A
rational and equal
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B
rational and distinct
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C
irrational and equal
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D
cannot be determined
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Solution
The correct option is B rational and distinct (b+c)x2−(a+b+c)x+a=0 Δ=(a+b+c)2−4(b+c)a =a2+b2+c2+2ab+2bc+2ca−4ab−4ac =a2+b2+c2−2ab+2bc−2ac =(a−b−c)2>0 as b+c≠a Δ is a perfect square and positive. Hence, the roots are rational and distinct.