Find the polynomial of lowest degree having leading coeffici

Find the polynomial of lowest degree having leading coefficient 1, real coefficients with a zero of 3 (multiplicity 2), and zero 1 - 5i. P(x) = For the following, find the function P defined by a polynomial of degree 3 with real coefficients that satisfies the given conditions. Two of the zeros are 4 and 1 + i. P(2) = 16

Solution

1)1-5i is zero ==>1+5i is also a zero since coefficients area real

polynomial is of form P(x)=(x-3)²(x-(1-5i))(x-(1+5i))

polynomial is of form P(x)=(x²-6x+9)(x-1+5i)(x-1-5i)

polynomial is of form P(x)=(x²-6x+9)((x-1)²-(5i)²)

polynomial is of form P(x)=(x²-6x+9)((x-1)²+25)

polynomial is of form P(x)=(x²-6x+9)((x²-2x+1)+25)

polynomial is of form P(x)=(x²-6x+9)(x²-2x+26)

polynomial is of form P(x)=x²(x²-2x+26)-6x(x²-2x+26)+9(x²-2x+26)

polynomial is of form P(x)=x⁴-8x³+47x²-174x+234