InterviewSolution
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InterviewSolution
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The polynomial `f(x)=x^4+a x^3+b x^3+c x+d`has real coefficients and `f(2i)=f(2+i)=0.`Find the value of `(a+b+c+d)dot` |
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Answer» Correct Answer - 9 If a polynomial has real coefficients, then roots occur in complex conjugate and roots are `pm 2i, 2 i.` Hence. ` f (x) = (x + 2i) (x - 2i) (x -2-i)(x -2-i)` `therefore f(1) = (1 + 2i) (1 + 2i) (1 - 2-i)(1 - 2 + i)` ` 5xx2 = 10 ` Also, ` f(1) = 1 + a + b + c + d` `therefore 1 + a + b + c + d = 10` `rArr a + b + c + d = 9` . |
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