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Consider the quadratic equation `nx^(2) +7 sqrt(nx)+n=0`, where n is a positive intergar. Which of the following statements are necessarliy correct ? I. For any n, the roots are distinct. (II) There are infinitely many values of n for which both roots are real. (III) The product of the roots is necessarlity an integer.A. III onlyB. I and II onlyC. II and III onlyD. I, II and III |
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Answer» Correct Answer - b `D=49n-4n^(2)` `=n(49-4n)` `Dne0 "for any n" in I^(+)` so roots are distinct. for roots to be real `D ge 0` So `n le49/4` so n can be { 1,2,3 ……….12 } Clearly product of the roots is 1. |
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