Answer to Question #43006 in Calculus for shasha

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 + 3i

f(x) = x4 - 6x3 + 12x2 - 90x + 416

f(x) = x4 - 45x2 + 180x - 416

f(x) = x4 - 35x2 + 180x - 416

f(x) = x4 - 6x3 - 12x2 + 90x - 416


help me please and show work

Answer 1

As 4, -8, 2+3i are zeros of polynomial, 2-3i is also zero. To find such polynomial write the next expression: (x-4)(x+8)(x-(2+3i))(x-(2-3i))=x^4-35x^2+180x-416.

Answer. x^4-35x^2+180x-416.