How do you write a polynomial function of least degree given the zeros -2i, #2+2sqrt2#?

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Answer 1 · 2018-03-05T11:26:15

#ax^2-2ax(sqrt(2)-i)-4iasqrt(2)#

If the roots to a polynomial are #alpha# and #beta#

Then:

#(x-alpha)(x-beta)# are factors of the polynomial.

So:

#a(x-(-2i))(x-2sqrt(2))#

Where #a# is a multiplier.

#a(x^2-2xsqrt(2)+2ix-4isqrt(2))#

#ax^2-2ax(sqrt(2)-i)-4iasqrt(2)#

This has a complex coefficient, since only one imaginary root was specified. To have real coefficients the roots must be complex conjugates.