Answer:
this polynomial function is x³ - 9x² + 25x - 25 = 0. The other root of the polynomial is (2- i). Given Suppose one of the roots of the polynomial function is complex. The roots of the function are 2 + i, and 5. What is the complex conjugate theorem? The complex conjugate root theorem states that if f(x) is a polynomial with real coefficients and a + ib is one of its roots. Where a and b are real numbers.A real coefficient polynomial P(x), if (a + ib) is a root then (a - ib) will also be a root of P(x). The roots of the function are 5, (2+i), (2 − i). Then, The equation for this polynomial function is; (x - 5) x (x (2+i)) x (x - (2-1)) = 0 - (x - 5) × (x − 2 − i) × (x − 2 + i) = 0 - - - (x − 5) × ((x − 2)² — (i)² = 0 - (x − 5) × (x² - 4x + 5) = 0 x(x² - 4x + 5) — 5(x² − 4x + 5) = 0 x³9x² + 25x - 25 = 0Hence, The equation for this polynomial function isx³ 9x² + 25x 25 = 0.
Step-by-step explanation: