Question

Write a polynomial function of least degree with integral coefficients that has the
given zeros. 3i, -1, 0

Answer 1

A polynomial function of least degree with integral coefficients that has the

given zeros  $f(x)=x^4+x^3+9x^2+9x$

Given

Given zeros are 3i, -1  and 0

complex zeros occurs in pairs. 3i is one of the zero

-3i is the other zero

So zeros are 3i, -3i, 0 and -1

Now we write the zeros in factor form

If 'a' is a zero then (x-a) is a factor

the factor form of given zeros

$\:\left(x-3i\right)\left(x-\left(-3i\right)\right)\left(x-0\right)\left(x-\left(-1\right)\right)\\\left(x-3i\right)\left(x+3i\right)\left(x-0\right)\left(x+1\right)$

Now we multiply it to get the polynomial

$x\left(x-3i\right)\left(x+3i\right)\left(x+1\right)\\x\left(x^2+9\right)\left(x+1\right)\\x\left(x^3+x^2+9x+9\right)\\x^4+x^3+9x^2+9x$

polynomial function of least degree with integral coefficients that has the

given zeros  $f(x)=x^4+x^3+9x^2+9x$

Learn more : brainly.com/question/7619478