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# Answer to Question #42523 in Calculus for shasha

Question #42523
Write a polynomial function of minimum degree with real coefficients whose zeros include those listed. Write the polynomial in standard form.
4, -14, and 5 + 8i

f(x) = x4 - 362.5x2 + 1450x - 4984

f(x) = x4 - 9x3 + 32x2 - 725x + 4984

f(x) = x4 - 67x2 + 1450x - 4984

f(x) = x4 - 9x3 - 32x2 + 725x - 4984

show work and explain it to me please

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Assignment Expert
15.11.15, 11:04

Dear emma!
Thank you for leaving a comment. It is known that i*i=-1. Since
(a-bi)*(a+bi)=a*a+abi-bi*a-bi*(bi)=a*a+(abi-abi)-b*b*(i*i)=
=a*a-b*b*(-1)=a*a+b*b.
In this question a=5, b=8.
Next, (x-5-8i)(x-5+8i)=(x-(5+8i))*(x-(5-8i))=x*x-(5-8i)x-(5+8i)x+(5+8i)*(5-8i)=x*x+x*(-5+8i-5-8i)+(5*5+8*8)=
=x*x-10x+89

emma
13.11.15, 20:43

how did u get rid of imaginary #s