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

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

campbell_st · Answer

well the zero 2 + 5i is a complex zero and so has a conjugate of 2 - 5i

which means 

(x - (2 + 5i) and (x - (2 - 5i)) are factors of the polynomial 

so there is a quadratic factor of 

$$(x^2 + 4x + 29)$$

the other real zeros give the other factors

x = 4  means (x -4) is a factor 

x = -8  means (x + 8) is a factor. 

so the polynomial is 

$$P(x)= (x -4)(x+8)(x^2 + 4x + 29)$$

just expand it out

anonymous · Answer

Wow! Thank you!