InterviewSolution
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InterviewSolution
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If `a in (-1,1),`then roots of the quadratic equation `(a-1)x^2+a x+sqrt(1-a^2)=0`area. realb. imaginaryc. both equald. none of theseA. realB. imaginaryC. both equalD. none of these |
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Answer» Correct Answer - 1 `(a - 1) x^(2) + ax + sqrt(1 - a^(2)) = 0` `therefore D = a^(2) - 4(a - 1) sqrt(1 - a^(2))` `= a^(2) - 4a sqrt(1 - a^(2)) + 4 sqrt(1 - a^(2))` `= (a - 2 sqrt(1 - a^(2)))^(2) + 4sqrt(1 - a^(2))(1 - sqrt(1 - a^(2)))` `ge 0` for `a in (-1, 1)` Hence roots are real but not equal. |
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