Multiple Choice Questions on If the roots of the equation a2 minus bc x2 2 b2 minus ac x c2 minus ab 0 are equal where b ne 0 the........... for CDS Exam Preparation

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Multiple Choice Questions

If the roots of the equation a2 minus bc x2 2 b2 minus ac x c2 minus ab 0 are equal where b ne 0 the...........

Quantitative Aptitude (CDS) Quadratic Equations
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    If the roots of the equation (a2 − bc)x2 + 2(b2 −ac)x + (c2 − ab) = 0 are equal, where b≠0, then which one of the following is correct?

    a+b+c=abc

    Incorrect Answer

     a2 + b2 + c2 = 0

    Incorrect Answer

    a3 + b3 + c3 = 0

    Incorrect Answer

    a3 + b3 + c3 =3abc

    Correct Answer
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    Explanation:

    (a2 − bc)x2 + 2(b2 − ac)x+ (c2 − ab) = 0
    The given roots are equal, and then D must be zero
    [2(b2 − ac)]a2 − 4(a2 − bc)(c2 − ab) = 0
    ⇒ 4b4 − 12ab2c + 4bc2 + 4a3b = 0
    a3 + b3 + c3 = 3abc

    By: Munesh Kumari
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