Question

Write a polynomial function of least degree that has the roots x = 0 and x = (2 – i) and a leading coefficient of 1.

Answer 1

To write a polynomial function of least degree with the given roots, we can use the fact that if a polynomial function has a root at x = a, then (x - a) is a factor of the polynomial. Therefore, with roots at x = 0 and x = (2 - i), the polynomial function can be expressed as P(x) = (x - 0)(x - (2 - i)). The polynomial function of least degree with the given roots and a leading coefficient of 1 is P(x) = x^2 - 2x + ix.

Step-by-step explanation:

To write a polynomial function of least degree with the given roots, we can use the fact that if a polynomial function has a root at x = a, then (x - a) is a factor of the polynomial. Therefore, with roots at x = 0 and x = (2 - i), the polynomial function can be expressed as:

P(x) = (x - 0)(x - (2 - i))

Expanding this, we get:

P(x) = x(x - 2 + i)

Simplifying further, we obtain:

P(x) = x^2 - 2x + ix

So, the polynomial function of least degree with the given roots and a leading coefficient of 1 is P(x) = x^2 - 2x + ix.