Question

Write a polynomial function of minimum degree with real coefficients whose zeros include those listed. Write the polynomial in standard form. 4, -8, and 2 + 5i

Answer 1

$x_1=4, x_2=-8, x_3=2+5i, x_4=2-5i$

$y=a(x-x_1)(x-x_2)(x-x_3)(x-x_4)$

$y=a(x-4)(x+8)(x-2-5i)(x-2+5i)$

$y=a(x^2+4x-32)(x^2-4x+9)$

$y=a(x^4+4x^3-32x^2-4x^3-16x^2+128x+9x^2+36x-288)$

$y=a(x^4-39x^2+164x-288)$ , $a\neq 0$