Roots and Zeros 5.7.

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Presentation transcript:

Roots and Zeros 5.7

We know: the degree of the equation tells you the number of solutions imaginary solutions come in pairs

New info: if an imaginary number is a zero, then it’s conjugate is also a zero so, if 3i is a solution, – 3i is also a solution

Writing polynomial functions from zeroes Example 1: Write a polynomial function of least degree that has real coefficients and has the roots 3, 2, –4.

Example 2 Write a polynomial function of least degree that has real coefficients and a leading coefficient of 1 and has the roots 1 and 5i.

Writing polynomial functions from zeroes Example 3: Write a polynomial function of least degree with integral coefficients, the zeros of which include -3, 2, and – 7i.