SOLUTION: Write a polynomial function of minimum degree with real coefficients whose zeros include those listed. Write the polynomial in standard form.
7, -11, and 2 + 8i
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-> SOLUTION: Write a polynomial function of minimum degree with real coefficients whose zeros include those listed. Write the polynomial in standard form.
7, -11, and 2 + 8i
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Question 1100942: Write a polynomial function of minimum degree with real coefficients whose zeros include those listed. Write the polynomial in standard form.
7, -11, and 2 + 8i Found 2 solutions by stanbon, KMST:Answer by stanbon(75887) (Show Source):
You can put this solution on YOUR website! Write a polynomial function of minimum degree with real coefficients whose zeros include those listed. Write the polynomial in standard form.
7, -11, and 2 + 8i
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2-8i is also a zero
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f(x) = (x-7)(x+11)((x-2)-8i)((x-2)+8i)
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f(x) = (x-7)(x+11)((x-2)^2+64)
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f(x) = (x-7)(x+11)(x^2-2x+68)
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Cheers,
Stan H.
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You can put this solution on YOUR website! If complex number is a zero of a polynomial with real coefficients,
so is the conjugate complex number, .
So, we know four zeros of the function,
and for each , there must be a factor of the form .
As a consequence, the simplest polynomial function of minimum degree,
with real coefficients, and including those four zeros is .
Now, we just have to simplify and multiply.
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