Question

Write a polynomial function of minimum degree with real coefficients whose zeros include those listed. Write the polynomial in standard form.
4, -14, and 5 + 8i

Answer 1

If 5 + 8i is a zero, then 5 - 8i must also be a zero.
Now combine the zeros and multiply
\[f(x)=(x-4)(x+14)(x-5+8i)(x-5-8i)\]

Answer 2

f(x)=(x−4)(x+14)(x−5+8i)(x−5−8i)

Answer 3

x^4-9x^3

Answer 4

how would i do the rest

Answer 5

id either get 725x or 1450x

Answer 6

I'm not sure how you got x^4-9x^3. You need to multipliy these using the distributive property. Start with (x−5+8i)(x−5−8i) to eliminate the imaginary parts

Answer 7

x^2-5x-8ix-5x+25+40i+8ix-40i

Answer 8

you're missing -64i², which simplifies to 64. Now combine like terms. All the parts with i will cancel out

Answer 9

x^2-10x+25-64i^2+81x

Answer 10

there's no 81x. Just \(x^2-10x+25-64i^2\) and -64i² = 64. So once you combine it's
\[x^2-10x+89\]

Answer 11

Set that off to the side and multiply (x-4)(x+14)

Answer 12

x^2+14x-4x-56
x^2+10x-56

Answer 13

Right :) so now all that's left is to multiply the two quadratics
\[(x^2-10x+89)(x^2+10x-56)\]

Answer 14

(x2−10x+89)(x2+10x−56)
x^4+10x^3-56x^2-10x^2+560+89X^2+890x-4989

Answer 15

x^4+10x^3+23x+890x-4429

Answer 16

you missed a term (-10x)(10x) and 89*56 = 4984. Altogether it should be
\[x^4+10x^3-56x^2-10x^3-100x^2+560x+89x^2+890x-4984\]

Answer 17

x^4+67x^2+1450x-4984

Answer 18

C
thank you!

Answer 19

\[x^4-67x^2+1450x-4984\]
yes C