JEE Main & Advanced Mathematics Complex Numbers and Quadratic Equations Question Bank Solution of quadratic equations and Nature of roots

  • question_answer
    Roots of the equations \[2{{x}^{2}}-5x+1=0\], \[{{x}^{2}}+5x+2=0\] are

    A) Reciprocal and of same sign

    B) Reciprocal and of opposite sign

    C) Equal in product

    D) None of these

    Correct Answer: B

    Solution :

    We have that, if roots of \[a{{x}^{2}}+bx+c=0\]are\[\alpha ,\beta \], then the roots of \[c{{x}^{2}}+bx+a=0\]will be \[\frac{1}{\alpha },\frac{1}{\beta }\] and hence roots of \[c{{x}^{2}}-bx+a=0\]will be\[-\frac{1}{\alpha },-\frac{1}{\beta }\].


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