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| Math Central | Quandaries & Queries |
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Question from Lan, a student: If b and c are real numbers so that the polynomial (x^2) + bx + c has 1 + i as a zero, find b + c. |
Hi Lan,
Since your polynomial x2 + bx + c has real coefficients and 1 + i is a root then 1 - i is a root also. Substitute 1 + i and 1 - i into the equation x2 + bx + c = 0 and you will obtain two equations in b and c which you can solve for b and c. Once you have numeric values for b and c you can use the quadratic formula to find the root of x2 + bx + c and hence verify your solution.
Penny
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