InterviewSolution
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InterviewSolution
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Let `A={a in R}`the equation `(1+2i)x^3-2(3+i)x^2+(5-4i)x+a^2=0`has at least one real root. Then the value of `(suma^2)/2`is_______. |
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Answer» Correct Answer - 18 `A= (1+ 2i)x^(3) - 2(3 + i) x^(2) + (5-4i)x + 2a^(2) = 0` Let the real root of equations be `alpha`. Then `(1+2i) alpha^(3) -2(3+i) alpha^(2) + (5-4i) alpha + 2alpha^(2)= 0` Equating imaginary part zero, we get `2apha^(3) - 2alpha^(2) - 4alpha = 0` ` rArr or alpha(alpha^(2) - alpha -2) = 0` `rArr alpha = 0 or alpha = - 1,2` Now equating real part zero, we have `alpha^(3) - 6alpha^(2) + 5alpha+ 2alpha^(2) = 0` " `alpha = 0 rArr a =0` ` alpha= -1 rArr a = pm sqrt(6)` `alpha = 2 rArr alpha = pm sqrt(3)` `rArr sum alpha^(2) = (0)^(2) + (+sqrt(6))^(2) + (-sqrt(6))^(2) + (+sqrt(3))^(2)+ (-sqrt(3))^(2)` `= 18` |
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