If a+b+c=0, then the roots of the equation c2−abx2−2a2−bcx+b2−ac=0 are

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real and equal

imaginary

real and unequal

None of these

answer is D.

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Detailed Solution

D=4a2−bc2−b2−acc2−ab=4a4+b2c2−2a2bc−b2c2−ac3−ab3+a2bc=4aa3+b3+c3−3abcD=4a(a+b+c)a2+b2+b2−ab−bc−ac=0 [ as a+b+c=0]Hence roots are real and distinct.

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