InterviewSolution
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InterviewSolution
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The quadratic equation `p(x)=0`with real coefficients has purely imaginary roots. Then the equation `p(p(x))=0`hasonly purely imaginary rootsat real rootstwo real and purely imaginary rootsneither real nor purely imaginary rootsA. only purely imaginary rootsB. all real rootsC. two real and two purely imaginary rootsD. neither real nor purely imaginary roots |
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Answer» Correct Answer - D If quadratric equation has purely imaginary roots, then coefficient of x must be equal to zero. Let `p(x)=ax^(2)+b` with a, b of same sing and `a, b in R.` Then `p[p(x)=a(ax^(2)+b)^(2)+b` P(x) has imaginary roots say ix. Then , also `ax^(2)+b in Rand (ax^(2)+b)^(2)gt0` `a (ax^(2)+b)^(2)+b ne0, AAx` Thus, `p[p(x)] ne0, AAx` |
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