Question

Find a polynomial of degree 4 with integer coefficients which has zeros of 3i and 4 if 4 has multiplicity of 2

Answer 1

firstly remember that when a complex number is a root for polynomial then

conjugate of that complex number will be the so \(x=3i\) and \(x=-3i\) are roots

so the polynomial includes this term \((x-3i)(x+3i)\)


\(x=4\) is aroot with multiplicity of 2 so the polynomial includes this term \((x-4)^2\)