SOLUTION: write the polynomial function of minimum degree in standard form that has zero -1 and 2i. Assume the leading coefficient is 1.

Question 1155804: write the polynomial function of minimum degree in standard form that has zero -1 and 2i. Assume the leading coefficient is 1.
Found 3 solutions by MathLover1, Boreal, ikleyn:
Answer by MathLover1(20850)   (Show Source): You can put this solution on YOUR website!

function of minimum degree in standard form that has zeros

-> since complex zeros come in pairs, you also have

then

.....use the rule for difference of squares

Answer by Boreal(15235)   (Show Source): You can put this solution on YOUR website!
-2i and +2i are roots, since complex roots are conjugate
-1 is other,
(x+1)
x=2i, x= -2i. (x^2+4)=0
(x+1)(x^2+4)
x^3+x^2+4x+4=0

also,
if first coefficient is 1 then
x=(1/2)(-b+/- sqrt(b^2-4ac)
the discriminate is -16 and b is 0
therefore -4ac=-16
a is 1, c=4
(x^2+4)

Answer by ikleyn(52803)   (Show Source): You can put this solution on YOUR website!
.
write the polynomial function of minimum degree in standard form that has zero -1 and 2i. Assume the leading coefficient is 1.
~~~~~~~~~~~~~~~~~

Complex zeroes go in conjugate pairs if and only if the polynomial has real coefficients. But the problem does not state it --- therefore both solutions of the two other tutors are IRRELEVANT.

RELATED QUESTIONS
Write a polynomial function f of least degree that has a leading coefficient of 1 and the (answered by stanbon,ikleyn)
Write a polynomial function f of least degree that has a leading coefficient of 1 and... (answered by Boreal)
Write an equation of least degree with a leading coefficient of 1 of a polynomial... (answered by josgarithmetic)
write a polynomial function with leading coefficient a=1 that has the given zeros. a.... (answered by josgarithmetic)
write a polynomial funtion of least degree that has real coefficients, the given zeros,... (answered by Alan3354)
Write a polynomial function f(x), in standard form, of the least degree that has real... (answered by ReadingBoosters)
Write a polynomial f(2) of least degree in standard form that has rational coefficients, (answered by josgarithmetic)
Write a polynomial function of minimum degree with real coefficients whose zeros include... (answered by greenestamps)
Write a polynomial function of minimum degree with real coefficients whose zeros include... (answered by MathLover1)