Find a cubic polynomial in standard form with real coefficients, having the zeros 4 and 5i. let the leading coefficient be 1.

If one of our zeros is 4, then the factor is x-4.  If the second zero is 5i, then the conjugate root theorem says there HAS to be a root that is -5i.  So our 3 factors are (x-4)(x+5i)(x-5i).  We will FOIL out these factors to get the polynomial.  Let's start with the ones that contain the imaginary numbers.  Doing that mutliplication we get x^2-25i^2.  i^2 is equal to -1, so what that expression simplifies down to is .  Now we will multiply in that last factor of (x-4):  .  FOILing out we have .  There you go!

Answer:

$4034.40

step-by-step explanation:

the perimeter of the field is the sum of the lengths of the four sides:

47 yd + 158 yd + 47 yd + 158 yd = 410 yd

the cost of 3 ft (1 yd) of fence is 3×$3.28 = $9.84.

so the cost of jake's wood perimeter fance is

(410 yd) × ($9.84 /yd) = $4034.40