Question

Based on the graph how many real number solutions to the equation X^3+6x^2+12x+8=0have

Answer 1

ANSWER

One real root.

EXPLANATION

The graph of the function

$f(x) = {x}^{3} + 6{x}^{2} + 12x + 8$

is shown in the attachment.

According to the Fundamental Theorem of Algebra, this function must have 3 roots including real and complex roots.

The x-intercepts gives the number of real roots.

Observe that the graph has only one intercept.

This implies that, the equation:

${x}^{3} + 6{x}^{2} + 12x + 8 = 0$

has only one real solution.