Question

5/4, 1 + square root of 3 write the polynomial function of least degree with integral coefficients that has the given zeros

Answer 1

4x³ - 13x² + 2x + 10 = 0

Explanation:

(x - 5/4) [x - (1 + √3)] [x - (1 - √3)] = 0

4(x - 5/4) [x - (1 + √3)] [x - (1 - √3)] = 0

(4x - 5) [x - (1 + √3)] [x - (1 - √3)] = 0

(4x - 5) [x - 1 - √3] [x - 1 + √3] = 0

(4x - 5) [(x - 1) - √3] [(x - 1) + √3] = 0

(4x - 5) [(x - 1)² - 3] = 0

(4x - 5) (x² - 2x + 1 - 3) = 0

(4x - 5) (x² - 2x - 2) = 0

4x³ - 5x² - 8x² + 10x - 8x + 10 = 0

4x³ - 13x² + 2x + 10 = 0