Question

How many and of which kind of roots does the equation f(x)=x3+2x2+4x+8 have?
A. 1 real; 2 complex
B. 3 real
C. 2 real; 2 complex
D. 2 real; 1 complex

Answer 1

The equation has 3 solutions consisting of 1 real; 2 complex

Roots of a polynomial

Polynomial are expressions that has a leading degree of 3 and above. Given the polynomial equation below;

f(x)=x^3+2x^2+4x+8

The roots is the point where f(x) = 0

x^3+2x^2+4x+8 = 0

Group

(x^3+2x^2)+(4x+8) = 0

Find the factors

x^2(x+2)+2(x+2) = 0
(x^2+2)(x+2) = 0

Find the roots of the equation

x^2+2 = 0

x^2 = -2

x = ±√-2
x = ±√2 i

Similarly

x+2 = 0

x = -2

Hence the equation has 3 solutions consisting of 1 real; 2 complex

Learn more on zeros of polynomial here: https://brainly.com/question/11514041

#SPJ1