InterviewSolution
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InterviewSolution
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Let `f(x)=a x^2+b x+a ,b ,c in Rdot`If `f(x)`takes real values for real values of `x`and non-real values for non-real values of `x`, then`a=0`b. `b=0`c. `c=0`d. nothing can be said about `a ,b ,cdot`A. `a = 0`B. `b = 0`C. `c = 0`D. nothing can be said about a, b, c. |
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Answer» Correct Answer - 1 Suppose `a ne 0`. We rewrite f(x) as follows : `f(x) = a{x^(2) + b/a x + c/a}` `= {(x + (b)/(2a))^(2) + (4ac - b^(2))/(4a^(2))}` `f(-(b)/(2a) + i) = a{(-(b)/(2a) + i + (b)/(2a))^(2) + (4ac - b^(2))/(4a^(2))}` `= a{-1 + (4ac - b^(2))/(4a^(2))}`, which is a real number This is against the hypothesis. Therefore, a = 0. |
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