Question

a 5. Construct a third degree polynomial with the following properties: real coefficients; two of the zeros are * = 2- i and = 1; and the leading coefficient is 2. You may keep your answer in factored form.

Answer 1

Hello,

Explanation:

As coefficients are real, if 2-i is a zero, 2+i is also a zero

P(x)=k*(x-1)(x-(2-i))*(x-(2+i))=k*(x-1)(x²-4x+5)

leading coefficient=2, so k*(-1)*5=2 => k=-2/5

P(x)=-2/5*(x-1)(x²-4x+5)