Final answer:
To write a polynomial in standard form with a zero of x = -1 + 5i and a leading coefficient of one, we have to consider the complex conjugate as well. The complex conjugate of x = -1 + 5i is x = -1 - 5i. Using these two zeros, the equation of the polynomial in standard form is x² + 2x + 26 = 0.
Step-by-step explanation:
To write a polynomial in standard form with a zero of x = -1 + 5i and a leading coefficient of one, we have to consider the complex conjugate as well. The complex conjugate of x = -1 + 5i is x = -1 - 5i. Using these two zeros, we can write the quadratic polynomial as (x - (-1 + 5i))(x - (-1 - 5i)) = 0. Simplifying this expression, we get x² + 2x + 26 = 0. Therefore, the equation of the polynomial in standard form is x² + 2x + 26 = 0.