Question

Write a polynomial function of the least degree that has roots of 3 and (4 + i).

Answer 1

Answer:

• x³ - 11x² + 41x - 51

Step-by-step explanation:

The least number of degree is 3 and the third root should be (4 - i) to make polynomial rational.

The polynomial is:

• (x - 3)(x - (4 + i))(x - (4 + i)) =
• (x - 3)(x² -x(4 + i + 4 - i) + (4 + i)(4 - i)) =
• (x - 3)(x² - 8x + 16 - (-1)) =
• (x - 3)(x² - 8x + 17) =
• x³ - 8x² + 17x - 3x² + 24x - 51 =
• x³ - 11x² + 41x - 51