If the polynomial has real coefficients, then the complex roots occur in conjugate pairs, so +3i is also a root. So,
your description is a bit muddy, but I'd say
y = (x-4)(x^2+9)(x-1)
That is degree 4. If you want x=1 to be of multiplicity 2, then that would be
y = (x-4)(x^2+9)(x-1)^2
Bu that is of degree 5, so maybe you don't need real coefficients, making possible
y = (x-4)(x+3i)(x-1)^2
form a polynomial with a degree of 4 zeros 4,-3i,1 and multiplicity 2
1 answer