SOLUTION: Find a polynomial function of least degree having only real​ coefficients, a leading coefficient of​ 1, and zeros of 3 and 2 plus i .
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-> SOLUTION: Find a polynomial function of least degree having only real​ coefficients, a leading coefficient of​ 1, and zeros of 3 and 2 plus i .
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Question 1126012: Find a polynomial function of least degree having only real coefficients, a leading coefficient of 1, and zeros of 3 and 2 plus i .
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if zeros are (real one) and (complex one), then you also have because complex zeros always come in pairs
since you have three zeros, a polynomial function of least degree will be a polynomial function of degree ...substitute given zeros
Given the three roots p, q, and r, one way you can find the equation is multiply out (x-p)(x-q)(x-r), as shown by the other tutor. With the two complex roots, the algebra gets a bit ugly.
So here is another way to find the equation that some students might find easier.
In the final equation (with leading coefficient 1)
,
the coefficient of the quadratic term is the opposite of the sum of the roots:
the coefficient of the linear term is the sum of the products of the roots two at a time:
and the constant term is the opposite of the product of the three roots:
