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Question

lf the roots of the equation (a2bc) x2+2(b2ca)x+(c2ab)=0 are equal, then the condition is

A
a+b+c=0
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B
a3+b3+c33abc=0
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C
a=0 or a3+b3+c33abc=0
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D
b=0 or a3+b3+c33abc=0
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Solution

The correct option is D b=0 or a3+b3+c33abc=0
Condition for roots of a quadratic equation to be equal is b2=4ac
(b2ca)2=(c2ab)(a2bc)
b4+c2a22ab2c=c2a2a3b+ab2cbc3
b(a3+b3+c33abc)=0
b=0 or a3+b3+c3=3abc

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