Write a polynomial equation of degree 2 in standard form given that one root 2 + 5i

x^2 - 4x + 29 = 0

Step-by-step explanation:

Complex roots occur as conjugate pairs.

So the other root will be  2 - 5i.

First write the equation  it in factor form:-

(x - (2 + 5i)) (x - (2 - 5i) = 0

(x - 2 - 5i)(x - 2 + 5i) = 0      Now expand:-

x^2 - 2x + 5ix - 2x + 4 - 10i - 5ix + 10i - 25i^2 = 0

x^2 -2x - 2x + 4 - 25*-1 = 0

x^2 - 4x + 29 = 0   (answer)

The equation that represents the height as a function of the time is:

f(x) = 34 + 2.625x, where x represent the amount of year since age 2

We need to find x such that f(x) = 50 that is:

34 + 2.625x = 50

x = 6 years rounded to integer

6 years after the age of 2 is 2 + 6 = 8 years.

Monique's son will be 8 years old and 50 inches tall.

Step-by-step explanation: