it says write a polynomial function of minimum degree in standard form with real coefficients whose zeros and their multiplicities include those listed: -1 (multiplicity 2), -2 -i (multiplicity 1). Can anyone help?
If you know the zero (root) of a function, you know a factor of it. Turn a zero into a factor by plugging the zero into (x - zero). For example, if 3 is a zero, then (x - 3) is a factor. Multiplicity just means how many times a particular factor is used. Multiplicity 2 means the factor is squared. So, take all your factors (you'll have 3 in your example) and multiply them together (or just write them side by side if you don't need to FOIL out) and you're done.
Thank you!
There's one more thing you'll need. If a real polynomial has a complex root, say a + bi, then it also has the root a - bi, called the complex conjugate of a + bi. So our polynomial actually has an additional root -2 + i, which is stealthily hidden in the list they gave.
thanks
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